The issue of whether you need a car when staying on site at Disney is a hot issue on these boards. IMO, if you're staying at a Disney resort and intending on only going to the parks and DTD, then you do not need a car. Disney transportation is great. Some people prefer to drive finding it easier to handle with children and lots of things they carry. Others find it takes less time than waiting for a bus, boat, monorail, etc. I think the time is about the same when you factor in walking to your car, getting through toll plazas, finding a parking spot, walking to the park, etc.
If you are staying off site I recommend renting a car. This is true even if it is a local hotel with busses to Disney. Many of these busses run on a set schedule. They'll have a few runs in the morning and a few runs around closing time. If you miss the bus or the times aren't convenient you're stuck with taking a cab. Disney transportation runs continuously every 15-20 minutes. It begins running at least one hour before the park opens and keeps running after the park closes. In the evening the busses run regularly to DTD until after the clubs close.