We don't put art requirements on submissions, we accept all forms of game art here.  Different games will each have different individual requirements, and the programmers requirements will differ from engine to engine.  Essentially each artist chooses which art style and level of fidelity they wish to create, and then they upload whatever they want.  

We ran a competition called the "liberated pixel cup" which used 16x16 assets,  so 16x16 is very popular here. If you're interested in expanding our library of 16x16 here are two collections of existing 16x16 art you could work into.

http://opengameart.org/content/oga-16x16-jrpg-sprites-tiles

http://opengameart.org/content/16x16

If you want to do other sizes, and you should feel free to, My advice is to have a look at some open source games you like the look of, and then mimic their art style. Most open source games will have publicly available art requirements.

@jimbolic: Hello and welcome! As p0ss said, there are no particular quality/quantity/format requirements for submissions, the matter is mostly left to the artists' common sense. Still, bart wrote some submission guidelines (that cover most type of assets, not only pixel art) worth reading.

As for getting started with game pixel art, I'd suggest you to read this tutorial and this (the latter is not much game-art-oriented, but it's quite useful in any case). If you have already done something in pixel art, you'll probably be already familiary with some of the concepts.

p.s. I think the Liberated Pixel Cup actually had 32x32 assets, which is another common tilesize (along with the above mentioned 16x16)

Yeah, the LPC and 16x16 assets were both OGA-backed projects, but independent of one another.

After submitting your art, I highly recommend adding useful tags as they will greatly improve the visibility of your work. Basically put yourself in the shoes of a game maker looking for art for her game; she will have very specific requirements for that art so if you tag accordingly, your art will appear at the top of the search results.

For pixel art, the tile size is a very obvious one, as 16x16 works poorly when upscaled to 32x32, and downscaling is poor too because pixel art is finicky like that. Another important one is perspective - top down, side view (platformer), isometric. Sometimes palette is important (e.g. the dawnbringer palette seems popular), but if you're not too picky you can always do a palette replacement.

Tags about the kind of game that the art will fit in, are generally useful. Staves and wizard hats don't fit in sci-fi games, hence tags like "sci-fi" or "fantasy" are good.

When you have room, include a few items in your art pack in the tags. A lot of the time, a game maker will be looking for a specific piece of art - maybe a statue, or a lamp - and including those in your tags will make you stand out. For example, you migh create a "military vehicles" art pack, but if you include "tank" and "jeep" in your tags, you'll get more hits. The best submissions I find via searching often have loads of tags.

So have as many tags as you can think of, especially those that are relevant for your audience.