I'd say 2 GB of VRAM is probably fine for most games out there. When you start getting into Skyrim and modding, 3 GB would be better. Anything over 3 I think is unnecessary unless you go into resolutions higher than 1080p or multi-monitors, etc.
The problem with thinking about the question in terms of resolution and multiple monitors, is that is doesn't consider the possibility game engines simply generating larger and more complex worlds, with a greater amount of more detailed objects displayed. It assumes that the amount of texture data required will remain fairly static in coming games, and that only increasing the size of the scene displayed in two dimensions will increase the demand.
The vram that is required to simply display the pixels of a given display size is only part of the consideration.
More powerful engines that render 'deeper' and more complex spaces will include more objects requiring texture data, and yet more to be cached, if you want to avoid the stuttering of texture loads as the scene changes. You can demonstrate this even in Skyrim (a pretty dated engine) by jacking up the ugrids and watching the vram demand climb as the world space grows. You can also see this with mods that add variety to flora and fauna, for example - more varied objects in the scene boost the vram requirement, even if their resolution is at the lower end. With boosted ugrids and a good card, you can also see how vram use can increase significantly, while still retaining solid framerates on current gpus.
The size of textures, like any digital images, is also not determined only by its X x Y size. It is also determined by the detail and complexity of the image, and the amount of degradation that is tolerated in the level of compression; there is scope for texture sizes to increase in ways other than sheer resolution.