Technically, the higher the resolution, the more RAM you require - but this amount is pretty insignificant today.. it was more an issue back in the day when 4MB of video memory was considered high end.. a 4 MB video card would let you display 1600x1200 resolution.. like I said, 4 MB is nothing today..
Today, at least for gaming, the RAM is used by the GPU for the computational work of manipulating and storing the textures processed by the card.. in theory, the more ram you have, the more textures it can store in memory for faster access if the game is written to support the higher amount of RAM.
Personally, I would go for 256MB unless you are the type that has lots of money and buys a new card every couple years. If you were looking at buying a new card in a year or two, you might want to stick with 128MB because you would buy a new card again soon anyway. If you don't like blowing $300 or so on the newest cutting edge card every year and want to eek out as much life out of your next purchase, spend the $300 or so on a nice 256MB+ card now.