1GB of VRAM is fine for 1920x1200. Above that then 2GB. For 3 monitors 4GB is recommended.
1920 x 1200 x 32bit (4) x 4 frames = 35.15625 MB for the frame buffer. Plus textures, which typically compress at 6:1 (or more).
So yes, <= 1GB of VRAM is still enough for many of today's games.
- 1GB of Video memory is enough for 6 to 8GB of textures.
If you're running Crossfire X or SLI with multiple monitors then I'd recommend 2GB.
Remember: It is not the amount of video memory that counts it is the speed of the video memory in MB/sec that counts!
Low end cards with 3GB are how many move their low end parts in volume, as people think more GB == better, when that is only maybe 15% of the picture.
Fairly safe with 2 gigs today, depending on game and mods. Next year the new consoles come out, which is presumed to carry more ram, and allow for higher usage of VRAM. I would say youd be safe for as long as your card will last before more demanding games are ported over from the new consoles to PC having 2 gigs at 1080, provided your card can actually use it all