You can capture all of the Pokémon possible in one version, which is a Master Ball Challenge. Capturing all 150/151 requires 2 actual copies of the games, plus the Mew glitch and capturing Missingno. for the latter. Do note that you have to use a camera to take pictures if you're playing the actual game.

If you really want to try for all 150/151 while emulating, you can perform the Mew Glitch for all of the ones you're missing. It's going to be a real pain in the ass though...

QwertyNinja: I didn't know about VBAdvance Link. Is it possible to do online battles that way? That would be awesome!