It's really personal preference, but for me, I'd never go without a car. I drive 500+ miles a week commuting to and from work and I still prefer to drive myself on vacation. I guess it's a freedom thing, maybe a bit of a control thing. If you don'd mind public transporation, and the caveats that come along with it (sometimes very crowded, tied to their schedule, places you can't get to, or at least not easily), then you may not need a car.
Other things to think about are whether or not you're sure you're only doing Disney, or if you really might want to explore the Orlando/Kissimmee area. We have a lot of fun hitting the Disney parks early in the morning, ducking out around noon when they're crowded and exploring around Orlando, grabbing a nice lunch, then returning to the parks later in the afternoon after the rest of the "early risers" have left.