Another rental car fan here! It isn't a neccessity, but it does come in handy! With a family of five - we need a van from one of the transport companies - although for a rental car - we fit just fine in a full size. As an Emerald Club member and a Disney Club Member - I usually can get a great deal with National - equal to or less than transportation between the airport and hotel!
We usually stay at the CR - and obviously - use the monorail/boats for transportation around the lagoon, and to MK/Epcot. We have found that the bus transportation isn't as fun from this area - the resorts share buses and especially the trip to Downtown Disney is awful!!! Took us over an hour standing up!
We just got back from a combo convention/Disney trip with 6 junior high students. I rented a car, even though our state delegation (about 50 people) had already rented bus transportation to/from airport and the 2nd hotel, since it was my daughter's birthday that week. I had promised to take her to the Prime Time Cafe for her birthday dinner - even though we would still be at the conference at that time.
Just an example of the time savings - We stayed at the All Stars for the Disney portion of our trip. One day my daughter left her pass in the room and realized it just as the bus was pulling up - I told my husband and the others in our group of 12 that we would meet them there with the car. After our day at AK - I hopped on the parking tram, at the same time that they headed to the bus stop. I arrived back at our room - showered, made notes on the day in my Passporter, and walked up to the Food Court for a mug refill, then settled down to enjoy my book in the AC - 45 minutes later - the rest of the crew arrived back at the room!
Also, one of the high school students in our delegation lost his plane ticket. Since I had the car - I was able to drive him and his advisor to the airport to obtain a replacement. Otherwise - they would have had to take care of that during prime time as we were checking in for our flight home - no time for errors that way!