According to AmigaWorld magazine, it is better to have a 2-meg video board then a 4-meg video board. When I find the article, I will post it. :-D
Damn, my 64MB graphics card must be really holding my system back, I should really upgrade to a Cirrus Logic 5446 2MB card for superior performance!
For 2D use only, there is always going to be an amount of memory which is just plain overkill, but that is relative to what resolutions you're wanting to use.
I'd say 2 - 4MB on a graphics card to do 800x600 effectively (as in, responsive as well) is adequate. 4 - 8MB for 1024x768. Keep going up like that, approximately, though I have no idea how well an average 8MB graphics card would do with resolutions above 1024x768, I made the jump from 4MB to 16MB with my first PC, and have only used 8MB graphics cards for very short periods of time.
The main factor however to a decent quality display (excluding the monitor) is the graphics chipset. IMO, not enough attention is paid to display clarity in graphics card reviews.
I had a PCI 2MB Cirrus Logic 5446 once (this is in a PC I'm talking about), IIRC I used it for 800x600x16-bit and it was "ok". IIRC it didn't like doing decent refresh rates (eg. 75Hz and above). I upgraded to a Permedia 2-based 4MB PCI card after that, and 1024x768x16bitx72Hz was then "ok" and lower res combinations were decent.