So, I don't know how many Android users there are on here, but I've seen enough comments and replied to quite a few people regarding it that I'd like to make a relatively informative post on the OS, covering mostly root related stuff and listing quite a few apps I personally use and recommend to people.
First off, should you root? If you have no idea what root is and are happy with your phone/device exactly the way it is then the answer is likely "no". If, however, you want to be able to do WAY more with your device than you even thought was possible though and aren't afraid to do a bit of reading and research, then the answer is a most definite "what the hell are you waiting for?!"
That said, I won't explain root. There are numerous websites and pages online that can do a much better job of explaining what it is than I can. What it isn't, necessarily, is for the faint of heart. Root is shockingly easy to get on most devices, but sometimes it does require some manual command typing to achieve. (Albeit the more popular the device you own, the easier it is to get root on it. Likely because someone has created a toolkit to do so, because even us "pros" like to automate things and save ourselves time.)
If you haven't heard of XDA-Developers, I suggest you familiarize yourself with it first and foremost. Especially if you want root or a custom ROM or anything like that. There are a few important things to know about the various forums though. First rule of XDA and the ROM community is DO NOT ask for ETAs on anything. DO NOT. I cannot emphasize that enough. The community is largely volunteer and no one wants or needs people saying "when is this going to be released" and "why haven't you released this yet" and things like that. I have seen too many good developers and generally helpful users quit the community because of people asking them that, so please do not do that. They are their doing things on their own free time, have the decency and respect to both not make things bad for them and give the people the recognition they deserve for their hard work. The second general rule is research, research, research. If you have any questions, search the threads. Someone else likely had the exact same question already and it's likely already been answered (multiple times). If you aren't willing to at least put in the effort to look for answers on your own you might find that people aren't necessarily willing to help you. Basically, why should they help if you won't help yourself? If you find that you have a question or issue that hasn't already come up then you can feel free to post it (assuming you've signed up and logged in as a user). People will generally be helpful, assuming you don't come off as brash or whiny or ungrateful.
Explaining a few things.
Custom Recovery. This is a non-stock recovery app that is accessible by a button combination pressed to turn on the device or through an app or even mod within the device if you want to reboot to recovery. The most popular ones are ClockworkMod Recovery (CWM) or Team Win Recovery Project (TWRP) recovery, both of which are available as touch based versions for numerous device. If you want to flash a custom ROM (or even a stock ROM with tweaks and mods added), you are definitely going to need a Custom Recovery. There's no room for debate on that front. On the bright side, once you have this installed on your device, you can back up everything and revert back to said backup in case something goes wrong down the line. You can also wipe your device entirely (the stock ROM) and replace it with something else like CyanogenMod or OmniROM or Paranoid Android.
I personally have TWRP installed and am on the stock Nexus 4 ROM, with a few tweaks and mods added per my needs. I'm running the latest version of Android, which is Kit Kat 4.4. To each their own though, not all ROMs are created equal and what works for me may not work for you and so on and so forth. That's the beauty of the XDA forums, there's almost certainly something on there for everyone. Like I said though, the more popular your device the more people who have it and are working on it and thus more custom ROMs, apps and so on and so forth.
Root. There are two versions, actually three now, or root. There is Superuser, which was the standard for quite a long time. There is SuperSU, which has become the defacto version of choice for most root users. Lastly, there is a version built into CyanogenMod, created by Koush. This last version is likely one that you will not run into unless you're planning to install CyanogenMod on your device.
I'm not going to go off more on those two main things, I could but I feel it is important that if you're going to attempt any of the really fun stuff that can be done with any Android device that people attempt to learn things on their own. This is for one very important reason, there won't always be someone there to hold your hand and fix potential screw-ups that may arise. So it's best to learn to do the necessary research and reading on one's own first and foremost.
EDIT: umataro42 and ShadowStarr both mentioned things I'd forgotten to include, oversight on my part. Adding them here.
Bootloader unlocking. This is VERY important when it comes to custom ROMs and root. As umtaro42 said, which I am very thankful for pointing out, before you can do any of the good stuff (installing custom recoveries, first and foremost) you need to unlock your bootloader. The difficulty of this varies depending on device. If you are with Verizon, well, I won't say it's impossible, but it's not going to be a cake walk. If you own a Nexus device this couldn't be any easier. Everything else falls in between. Most importantly, unlocking a bootloader WILL wipe your device. Entirely. (Except what's on your micro SD card, assuming your phone has a microSD card slot.) So if you even think that you might down the line want to install a custom recovery to change ROMs do this (unlocking the bootloader) before anything else. There are numerous guides and toolkits on how to do so and helping to do so online. So feel free to look them up, just keep your particular device in mind when doing the appropriate search. What works for one will not always work for another and it is incredibly easy to brick some devices more than others. (I stress that bricking devices is not a common thing, but it happens enough that it's a risk. Like everything else mentioned to this point, know the risk and proceed accordingly. You can't say you haven't been warned.)
Xposed Framework. This is an incredibly useful mod that has been around for some time now. Basically this allows you to change the framework to install any number of useful modules without having to change ROMs or go through any number of tedious steps and processes. It is entirely possible to remove the Xposed Framework and restore back to full stock should you be inclined to do so. Keep that in mind.
Also here is a collection of Xposed Modules for use once you've installed the appropriate framework. You can do anything and everything with these, from enabling additional features to removing geographical restrictions on your devices (by which I mean you can use Wallet no matter where you are or enable access to certain apps that would otherwise be unavailable in the Play Store). I could go on and on about the various modules, but this is already a seriously lengthy post so I won't. Like I said elsewhere, read up on it before implementing it.
But onward and upward as the kids say! Or as Bill Clinton would say...
Anyway, on to some apps I recommend and personally use.
(Google) Authenticator - 2 step verification. Basically, security. Everyone should be using this if they have a Gmail account.
BBC News - News. No one does the news like the BBC, at least not here in America. Straight forward reporting with no sensationalism. Can't beat that.
Cerberus - Anti-theft app. You can remotely lock your phone, wipe it (and its SD card) and so many other things using this app. All can be done from the web, if your device is misplaced and you (obviously) don't have access to it.
Circa - News app. Gives just summaries. Basically quick news fixes in a very beautiful looking app. Honestly, I get all my news through this app first and foremost before hitting the BBC one for additional information. (Which isn't to say Circa keeps things short. They do elaborate, but with summaries so you can skim.)
Falcon Pro - Twitter app by a great developer. Everything the Twitter app does now, this could do that ages ago. And it still has features the Twitter one doesn't.
Light Flow Lite or Lite Flow - LED control app. Let's you set the LED light (if your phone/tablet has one) to different colors and for different apps/notifications. You can tell if that email is important or not, if your significant other texted you or if it was your bestie, and so on and so forth.
Pocket - Save articles to Pocket and read later offline. Full articles/etc too. Not just snippets like some other apps. Great for when you see things you want to read, but don't have the time to at the moment.
PushBullet is another great app. You can push files, links, addresses, lists, etc to your phone. It's also got a Chrome and now Firefox extension, making doing so from your computer even easier and they've updated rather recently so you can send up to 25 MB files from the web interface. Not too mention the awesome fact that you can now do pushes in the other direction, from your phone to Chrome.
Random is another must have app. It'll give you quotes, generate passwords, allow for audio recordings, etc etc etc and then some. It's an amazingly useful all-in-one app. The developer is a great guy, been using his apps for a long time now.
Reddit Sync or Reddit Sync Pro - Reddit viewing app. Has a Cards UI look with sliding menus. Basically the latest Google/Android UI moves, this has it. I've actually taken to reddit way more because of this app. Productivity of course for work has taken a dive. Lol. But I do IT, so I have lots of down time where things are installing or tests are running and whatnot.
Tasker for sure is extremely useful! I have mine setup to turn on/off WiFi depending on when I come and go from home or work. I also have it setup to change the display brightness (to about 60%) from 6:30 AM to 10:00 PM. In addition to which I have it setup to change the audio levels throughout the day (morning at home, arrival at work, lunch break, back to work until I leave, at home and then bed). I've also set it up to automatically send "happy birthday" (and similar) text messages on the appropriate days (and at the appropriate times).
Okay, there are two pages in the Tasker Wiki where you can get information (and profiles that are mostly already setup) to get Tasker working just the way you want it with semi-minimal effort. If you can follow a step by step guide then you can set any of these up, even some of the more Advanced ones..
Here is where you can find already made profiles to import into Tasker. All you'll have to do is import any respective files and then change a handful of variables. It might seem complicated but it's very straight forward.
I setup Tasker to launch Google Play Music when a headset is connected, per my personal preference in music app. But follow the steps listed there you can setup any app to launch.
In addition to that I also have Tasker managing my WiFi settings (turning WiFi on and off) when I come and go from work or home. If you need additional locations to have WiFi toggled on and off it's also easy to do and you use the same guide and included profiles. (That's one of the more advanced ones and it was really easy to setup actually.)
Here is where you can find step-through and how-to guides. These tend to not be as easy as using already provided profiles, but if you just follow the guides you can get all the things setup that you want (from what's available there).
I have Tasker setup to automatically send "Happy Birthday" SMS. (Along with other things, like "happy anniversary" and other such things.)
Timely - Alarm clock app. Dime a dozen, right? Wrong! This one has every other alarm app beat. It can sync alarms across multiple devices, looks amazing and gives you pro features for free (if you just send an invite to a friend), but the full version (unlocked in-app) is only a buck or two if I remember correctly. Worth the price. But the free version more than does the job for most.
Titanium Backup is a life saver and will come in very handy if you decide to start trying out other ROMs and what have you. If you get the paid version it'll do one click backups and restores of your installed applications, among other things, making an already great app that much better. It also will allow you to create an update.zip of any apps you select, so if you do flash a new ROM you can get back up and running immediately after without having to wait for apps to download, install and then setup.
Tunable - Musical instrument tuning app. Simple. Beautiful looking. Perfect.
Unified Remote and Unified Remote Full - Want to control your computer from your phone? This does it. That's just a basic description, read the app description for the app to see just how much this can really do. It's not just another TeamViewer clone or something like that, in fact it's nothing even remotely similar. This one lets you control Netflix, Windows Media Player, Pandora, Google Music and your computer (among literally a ton of other things) all from your phone or tablet. (As long as you install the PC client and are on the same WiFi network.) This one app has been one of the best apps I've ever paid for, bar none.
7×7, Gyro and WordKick are all great games for killing time. Osmos HD and Cubes vs Spheres are as well (they just don't look as Holo as the other three, since these games require a little more graphics and interaction on your part).
Anyway, that about sums up a great many things. Depending on your device there may or may not be toolkits, as I stated earlier, that will let you install a custom recovery, root, push and pull files to and from your device, install ROMs for you and a number of other things. If you own a Nexus device (any of the phones or tablets from the N4 on up) you can go here to download a unified toolkit created by mskip that will do all those things I just mentioned, as well as unlock and lock your bootloader to enable all the good stuff that comes with owning a Nexus device. He is also the creator of a number of toolkits for a variety of Samsung device, all of which can be found here. (Devices include Note 2, S3, S3 Mini, Note 8.0, Note 10.1 2012 and Camera.) The basic gist of those devices is simple GUIs that make selecting what you want to do as easy to do as possible, at that point then providing you with incredibly easy to follow instructions for what is required on your part to enable the next given step. For the most part you don't have to know anything about ADB or Download Mode or anything like that, literally pick and choose and just do what the nice directions tell you to when it tells you to do it. That being said, don't just jump in and start going off because you think it's super easy. YMMV as we say on the forums. (Your mileage may vary.) You might be the one person whose device decides to explode and take the universe with it. Random things can and do happen, even to us "pros" and we screw up or have things screw up and we do our best to fix them or learn and apply the lessons the next time around.
If anyone has any questions or remarks or whatever feel free to leave a comment below. I'll do my best to answer things, keeping in mind that while I'm no expert I do know more than the average bear and have been tinkering with Android devices since the OG Evo. If it can be rooted though I've likely rooted it, which means most popular devices in the past year or two I've got hands on experience with and have likely rooted or ROM'd at some point or another.
Sorry for the extremely lengthy post. In the words of DrillPress, have a kitten!