My family always does. We live in North Carolina (and never went to WDW before we moved to NC), so it's not a huge drive for us. Average is about nine hours.
But, while I'm here, I might as well relay the "Twelve Hour WDW Drive" Story.
In 1998, my family of four (parents, brother, and I) went to WDW with our neighbors (Jan, Troy, Jan's son from her first marriage, Jan & Troy's two kids). We took two vans, but travelled together keeping one another within sight.
Sometime about two hours in, Troy's van started to overheat. We pulled over on the side of the interstate to let it cool for 20 minutes. And then drove for 20 minutes, cooled down for 20 minutes, drove for 20 minutes, etc.
Now, I was sleeping most of the time because a friend of mine from school (I was 15 at the time) had had his funeral the day before and I wasn't in the best of moods...I missed some of the details. But we stopped at a gas station/shop. Who's tow truck was broken down. That should have been a sign right there. There wasn't much they could do (I forget what the problem was exactly) and they recommended that we take it to a dealership.
We decided to pack everyone (including luggage) except Troy into my family's van. That's three adults, one 15 year old, two 12 year olds, a six year old and a five year old in a 1994 Ford Aerostar with one less seat than we had people. But it was cool because Jan decided to buy a bag of pork rinds and a six pack of beer at the gas station to ease her pain.
Apparently, after we split up, Troy's van was fine. He ended up driving back to NC, getting a few hours sleep, and driving back down to FL with his Lexxus the next day. To this day, I still don't know why.
Meanwhile, the rest of us are listening as Jan and Troy's six year old son asks, "Is that our hotel? Is that our hotel?" as we pass any Motel 6, etc. on the last hour and a half of our drive. Twelve hours after leaving, we're in WDW.
Yes, a long story for such a simple questions. But moral is, while driving can be cheaper than flying if it's an option, make sure you get a tune up before you leave! On our next trip my brother and I are taking a seperate car (mine!) from my parents. My entire tax return is going to make sure that that car is in tip top shape!