I thought you might have meant 1GB VRAM rather than system RAM. 2GB seems to be the minimum standard even for a budget gaming PC (especially on Vista). You can pick up 4GB for $20 or less if you watch the deals forum.
I played WoW when it was first released and beta on a P3 with 512MB RAM. It was very playable in most situations, except for large PvP raids with 60 - 80+ players fighting. Huge amounts of players on the screen would freeze the game for many seconds, so I could end up dead without ever seeing who or what hit me. It was still okay in non-combat situations with lots of players, like in cities. I wouldn't want to play any of the expansions on that old system though.