Most prequels are bad. This is due to many staying to close to the originals that they become pointless as we already know what's going to happen like The Thing prequel. Others are simply bad and result in massive inconsistencies and headaches such as with Star Wars Episodes 1-3.
However there are some that do surpass there original counterparts that deserve recognition. Interestingly, I found that video games seem to do the prequel better than any other art-form, I have no idea why this is and it is something that is worth discussion.
Note: due to never playing them, some video games I have kept back like Biosock Infinite, Metal Gear Solid 3 and Deus Ex: Human Revolution. Also, I didn't know whether or not to add the Godfather Part II or the AniMatrix into this list either as I didn't know whether they counted as a true prequels.
The Good, the Bad and the Ugly
Many don't realize that this is a prequel of a Fistful of Dollars and A Few Dollars More (and it's debatable on whether it was originally intended to be one), however there are many clues such as the man with no name gaining all his classic equipment in this film, the fact he lacks his injuries such as his lame right hand and the most obvious, the fact this is set during the American civil war while the other two are set after.
Regardless, the movie has surpassed it's previous, both critically and financially and has become one of the most popular and most influential movies of its genre.
X-Men: First Class
After two disasters of movies with X-Men: The Last Stand and X-Men Origins: Wolverine, First Class helped revive the movies series with a new cast and setting. We can also thank this for Days of Future's Past which in my opinion is the best of the series.
Interestingly, the movie could have been easily bad as like with many, it has the problem that we know what is going to happen. The fact that it was still able to be good with that is a testament to the quality of the writing and direction of the movie.
What would happen in a year without Superman, Batman and Wonder Woman? That's the question 52 asks.
52 was made after DC decided to jump all the books one year after the event Infinite Crisis with 52 filling in the missing year. It follows the events through the eyes of lesser known characters such as Booster Gold, Black Adam and many others.
Due to its brilliant storytelling and character development, 52 is usually rated incredibly highly in the comic-book industry. There is a reason why DC named the new continuity after it.
Dragon Ball Minus
Minus is a prequel for both the Dragon Ball series as well as Jaco the Galactic Patrolman. I won't go into detail as it's the most recent of all the works on the list and to avoid spoiling anyone, what I will say that it does a great job telling its story and it does make you feel sorry for Bardock & Gine as well as making the Saiyans feel more like an actual race (something a lot of other DB material fail at).
Star Wars: Knights of the Old Republic
Due to being set 4000 years before the films, this game had a lot more to work with and was freer to tell its own story. However, the fact that it was able to be better than the film prequels by far at a time when console RPGs were considered a laughable concept shows that it was one of the best prequels as well as one of the best games ever made.
Most of the Legend of Zelda series
A good chunk of the series is made of prequels, many of which are considered classics Such as the Ocarina of Time and Link to the Past. Why is up to debate as many suffer from knowing what's going to happen, but It could be that they all have their unique feeling to them thank to their individual gimmicks and like most good prequels isn't a slave to the source material.
Like KOTOR, Prime had a lot of mockery and hate from fans when it was announced due to it being a first person shooter in a series of side-scrollers (guess everybody forgot Duke Nukem 3D and is another example of how listening to fans is not always a good idea).
Again like most good prequels, Prime and its sequels is not a slave to the original game and as such, gives itself more freedom to develop its ideas.