A video card has two functions - 2D display (the windows desktop) and 3D display (i.e. games). Any memory over 8 meg (and in most cases over 4 meg) on a video card is for 3D functions only. So a 2 meg might be OK. If you are going to run in a high screen resolution (1024x768 or better) you would have to limit yourself to 256 colors.
However with RAM being so cheap, all new video cards coming out have 8, 16, 32 or more megs of video RAM. These cards are generally faster in 2D diplays just because the chipsets are newer.
I would suggest that for an older model PC without a AGP slot your 2 meg card would be fine. But if you are buying a new unit, get a new AGP card. You will find that even the cheap one have 8 megs or more of RAM. An if the unit you are looking has a built-in Video display that "shares" its RAM with the Video display, DON'T BUY IT. Only the cheapest home systems work this way, and it's indicative of headaches to come.