We always hire a car from the time we arrive at the airport and drop it back off at the airport. Yes you can get around Disney without one, but it is far more convenient to have one. Last time my wife went back from Magic Kingdom to Animal Kingdom Lodge, it took 40 minutes and involved a change at Animal Kingdom (all out of peak time, so got on the first bus each time), the journey by car is only 20 minutes. At peak times you may not get on the first bus, so another 10 minute or so wait for the next bus.
Also with a car you can eat off site, which not only saves a small fortune but gives you a wider choice.
If you want to go shopping or to Seaworld, Universal Studios or anywhere like that, a car is handy.
In my humble opinion a car for us pays for itself in the savings on taxis to other parks, shopping and we normally eat off site so that again saves a lot of money.