It's one thing with a household name, like Superman, or a somewhat familiar one, like Iron Man, but Guardians of the Galaxy is an exciting-looking movie without anything casual audiences would be familiar with. So do you need to read the comics before watching? Short answer: No.
As happens when delving into the rather byzantine connections between characters and situations in comics, someone asks whether the film may just be for comic fans. The truth is, you don't need to read comics to watch a comic movie, just as you don't need to watch the 80s Transformers cartoon to watch the Bayformers or have read Tom Clancy's Jack Ryan novels to watch The Hunt for Red October or Clear and Present Danger.
Take the floating head up top for example. That's Knowhere, and when it first appeared in Nova #8 (2007), readers had no idea what it was or where it came from (in fact, the second question still hasn't been answered) and that doesn't matter - a giant floating head space station is bad ass without explanation!
That said, if you want an explanation, the giant head comes from an apparently deceased member of the cosmic gods known as Celestials. These unknowable entities visit planets for reasons understood only by them, seed various races to vie for dominance, then return eons later to judge whether the surviving races are worthy of continued existence. Deep stuff, but needed for the movie? No. They'll probably never mention these guys in any detail (though the Eternals, who were created by the Celestials, would make for a helluva movie).
Guardians of the Galaxy is part of the Marvel Cinematic Universe - so while there may not be more then a few name drops and likely some cameo, it helps to know this exists in the same universe as Captain America: The Winter Soldier, Thor: The Dark World and Iron Man 3. Does that mean you need to watch those films first? No. It just means that, if you have watched (any or all) of those films, you'll likely get a slight chuckle when someone mentions Nick Fury or Stark Industries or something.
There will be some sort of tie-in in the second season of Marvels Agents of SHIELD. What form that connection will take is anybody's guess (although likely this blue guy from episode "TAHITI" will be tangentially related). Does that mean you need to watch that series? No. It might be fun if you're interested in seeing more Marvel later on though.
Thanos will be relevant in some way. Don't worry if you don't know who Thanos is yet - he was that purple guy smiling in the mid-credits scene of The Avengers - even if he doesn't actually appear in this film, he will be sufficiently explained in this or a later Marvel movie. Do you need to have watched The Avengers first? No. But why wouldn't you want to?
The Infinity Stones will be mentioned in some way. It goes without saying that the hinted at subplot running through Captain America: The First Avenger, The Avengers and Thor: The Dark World will be referenced in this film, since it involves the space-based objects of great power known as the Infinity Stones (or Infinity Gauntlet, or Soul Gems or various other titles). Do you need to know what they are? No. They'll be explained later, all that matters is that two of the six gems have been accounted for (EDIT: make that three possible gems accounted for. Thanks Ovidio for the reminder!). Big money suggests the sphere we see throughout the new trailer could be one of them.
Stan Lee will probably show up. Just as with other Marvel films, Stan is expected to have a cameo. He originally said he wouldn't because he didn't "create" the GotG, as he co-created other Marvel properties, but he did co-create Guardians member Groot. Is Stan Lee playing the same character he was in the other films? No. Despite some fan theories to the contrary, there is no indication Stan's characters are at all connected.
Everything else. Any additional info is just icing.
For example, when Rocket says, "ain't no thing like me, 'cept me," this is actually relevant to current comics. Rocket comes from a community of anthropomorphized animals, and while numerous rabbits and other species have multiple representatives, Rocket's the only raccoon we've seen so far. This gained significance in Guardians of the Galaxy Infinite Comic #2, when Rocket flipped his scat at someone's suggestion they'd seen "another one" like him on Rigel-7. Unfortunately the witness was assassinated before Rocket could learn more.
Speaking of Rigel, according to IMDB (however reliable that is), Glen Close's character is the Nova named Rael (no relation). Irani Rael is a member of a bulbous-headed people called the Colonizers of Rigel, although they can alter their proportions to appear more traditionally human.
Gamora and Drax could be sources of confusion for movie-goers as both are green-skinned, superstrong, assassins who have a personal hatred/connection to Thanos. Casual audiences may ask: Are they related? Are they from the same planet? Are they Hulks? The answer to all those questions is, "No." This might've been easier if they chose similar characters, like Moondragon or Adam Warlock - but maybe that's just me playing armchair producer.