Well, last year I drove by myself with my three kids (12, 5 and barely 3 at the time) from Northern Maryland to Clearwater, Florida. It was about 13 hours to Jacksonville where we spent the night, then another 4 or 5 to Clearwater.
Does that count since I had kids with me?
Sheri
Let’s see… Montgomery, Alabama to Denver, Colorado (or vice versa) three times @ 1400 miles each. Took two days, one of a really long drive - the second a mere 10 hours or so. Two different routes on this journey, about the same length.
After that, it was Montgomery, AL to Fairfax, VA and back within a month - 12-13 hour drive each way, not including naps at rest areas.
Bah! All you people counting trips that are split up over several days! 
How about from Philadelphia Pennsylvania to Arkadelphia Arkansas (a bit over 1200 miles) solo in twenty hours. That includes a half our or so hiding under an underpass in Tennessee during a heavy downpour, trying to figure out if the tornados reported on the radio were heading in my direction or not.
Eric
Bah! All you people counting trips that are split up over several days!
How about from Philadelphia Pennsylvania to Arkadelphia Arkansas (a bit over 1200 miles) solo in twenty hours. That includes a half our or so hiding under an underpass in Tennessee during a heavy downpour, trying to figure out if the tornados reported on the radio were heading in my direction or not.
I’ve done Philly to Orlando non-stop a couple of times too.
Eric
Ocean to ocean. Portland, ME to San Francisco, CA. It’s something like 3200 miles.
I did that once, and I’d do it again in a heartbeat.
Also, a regular trip was Portland to Niagara Falls. That’s somewhere in the 700 mile range. After doing int enough times it started to seem like a day-trip.
~1100 miles from Champaign, IL to Ft Lauderdale, FL. No sleep, stopping only for gas and toilet breaks. Entirely alone. About 15 hours.
More recently, Ocala, FL to Blacksburg, VA. Not sure how far, but it took about ten hours.
New Orleans to New Hampshire ~1900 miles in 2.5 days. I loved it but wish I took more time to enjoy it.
Spent a week vacation driving around Quebec by myself a few years back. Started from Boston, went through Maine and New Brunswick, around the Gaspe Peninsula, across the St Lawrence, and then up to Lac St. Jean. For whatever reason, I decided to come home at that point and drove all the way back to Boston in one day. I don’t remember the total mileage, but I think it was somewhere in the 1200-1500 range.
6000 miles from Barra de Navidad, Mexico to Hamilton, Montana via Houston and back. 1600 of those miles were on narrow 2 lane Mexican highways.
1360.8 miles from Vegas to Kansas City MO, then back again.
Also 2149.4 miles from Moundsville WV to Las Vegas. I was alone in a ryder truck but SO was driving a car, so not really alone. That and I had a dog or two in the cab with me.
I drove 3561 miles from NJ to Mt Rushmore and back in 5 days. I did the return trip (1725 miles) non-stop in about 28 hours.
Uphill both ways in the snow!
I think the longest trip I’ve made alone was from Boston to South Dakota (and back). I had a few days off from work, and decided to go see Mt. Rushmore on a spur of the moment thing.
I once drove all the way from Boston to West Virginia with a copy of Frank Zappa’s “Joe’s Garage” stuck in the cassette deck. That was, um, interesting.
1700 miles. Minneapolis to Fort Myers FL. It took me about 30 hours and no sleep or breaks at all. I stopped for drive-thrus and gas. Then I drove back three days later.
Now me! 
20 hours? It only took me 15 hours to make my 1,200 mile trip. (I could have taken less time, but I slowed down through Oregon.)
The trip back was about 1,400 miles from Bellingham to L.A. because I made a side trip to Hoquiam and then out to Westport for some smoked salmon. I had breakfast with a friend in Hoquiam and the rain and snow slowed me down somewhat (I had to stay below the hydroplaning threshhold) so it took me 23 hours nonstop (except for fuel, of course – no rest) to get back to Los Hideous from Bellingham. Not counting the side trip and breakfast, I still made pretty good time.
That should have been:
Not me!
Pre-caffeine post.
I once drove from Istanbul, Turkey to Lima, Peru in 23 hours non-stop, eating only Cheetos from vending machines, and pissing in empty Bud bottle on the way to save time.
And you’re not even going to swing by San Antonio to visit me and Aaron! 
Last year, I did over 4100 miles from St. Paul, MN to San Antonio, Texas. I got to meet lots of Dopers, and it was a great trip.
This coming weekend, I get to drive only 600-something miles from San Antonio to Biloxi, MS to visit Airman. I’m not doing the entire thing all at once, mostly for comfort reasons. I’m doing a little over half on Thursday, and the rest Friday morning. I should be able to make Biloxi by noon on Friday.
I’m also going to second whoever said that caffeine and junk food is bad on a long road trip. What I generally do is go to the supermarket beforehand and stock up on healthier munchies. This way, I know I’ve got something I can snack on that doesn’t involve quite so much sugar and grease.
Robin
Hudson Valley, NY to Singapore. 9,903 miles.
What? WHAT??? Oh, okay fine. Astoria, NY to Rockport, Maine. 11 hours. Slept in Salem, Mass with some old friends on the way up. On the way back, my freakin’ Chevy Astro minivan with the twitchy almost-dead carbeurator could not be shut down. I had to gas it with it running, and lock it running to run and hit the head.
11 hours, nonstop. It was miserable, however I did get to listen to “The Pillars of The Earth” by Ken Follett. Really helps out to have a good book on tape.
Cartooniverse
El Paso, Texas to Los Angeles. 13 hours, some of it feeling so drowsy I had to rest a few minutes on the side of the highway, only to be wakened by huge semis that rocked my car.