It depends on the card. The oldest video cards didn't even need a heat sink. (I'm talking about those with maybe 1MB of ram here folks...) Eventually the chips started getting really hot, and they needed at least a heatsink, if not a fan on it also. Why add a fan? To prevent the chip from overheating and dying. So in a way, a fan is needed, but only if the video chip needs one. I have seen many TNT2/ATI 7000/GF 5200s without a fan. The heatsink is large enough, and the chips emit such low levels of heat, that a fan isn't needed.
If you are looking at buying say a 7600GT with a fan and a 7600GT that lacks the fan, then the fanless 7600GT should be ok. The advantage is that it will be quieter then the one with the fan. The disadvantage is that they tend to cost a bit more then their fanned brothers. Money vs noise, thats something only you can answer.