We drive from Little Rock, AR with only stops from gas, dining/snacks or restroom breaks and the drive is ~1000 miles typically and takes around 14-15 hours or just less from door to door. Once we stopped overnight in Atlanta, GA adding to our expenses and really did not result in us being any more rested for our first day at Disney. When we were younger we preferred leaving late afternoon, switching off several times while she or I slept and usually meant the kids slept nearly all the way there and we arrived early in the morning to check into our resort. Once checked in we always had a relaxing day planned with pool time for the adults to relax and burn energy from the kids followed by a trip to DTD for them to scout souvenier ideas so we weren't constantly in the shops in the parks.
Today I prefer to drive during the day, leaving VERY early in the morning (3AM-4AM) which puts us in WDW around 8PM, we check-in, unpack, shower and get some rest so we can get up and out bright and early the next day. The kids have laptops, iPhones and iPads to keep them occupied so they are content to sit back, read or watch movies, and play games. We flew last summer, drove for Christmas and prefer the ease of flying but truely missed having the car. We spent a lot more money on flights ($1400), $200 shuttles/taxis to go off-site, and were restricted as we had to plan our times around a shuttle or cab to do off-site activities such as take our son to the outlet mall for school clothes shopping.
Having a car at Disney is not required to get around but makes dining at other resorts much easier, going out and about the Orlando area is much easier.