The Mountains to Sea Trail is a 930+ (1175?) mile long trail running the long way across North Carolina. As with many of these trails, much of the MST remains unfinished, but temporary connections on back roads and bike paths allow for a reasonably continuous route. Matt Kirk ran & hiked the trail in 24d3h50m on July 1-24, 2011. Kirk's trip was basically thru-hiker style, which we consider to be in the "self-supported" category, but apparently he did have some help from family in the second half (see below). His trip report is Matt's blog here. During the trip a website was set up to report on his progress. It includes links to articles, maps and photos.
Kirk has these things to say:
I wish to inspire people of all ages to break free of the self-destructive habit of driving everywhere and get out and use their original God-given vessels, their bodies, for transportation. There are a million excuses, and some of them are fairly legitimate, for remaining encapsulated inside a car. But the benefits of walking, running and biking are undeniable.
I like to hike.
Diane Van Deren tackled the MST in May-June 2012 as a fully supported, ultrarunning style adventure, sponsored by The North Face. She completed the route in 22d5h3m, on June 1, 2012. An article on her run from the Charlotte Observer is here.
Note that the MST is an evolving trail. Each year road sections are replaced by trail, and according to the MST website "The current  route of the MST includes 680 miles of trail and about 500 miles of connecting roads. Our goal is a continuous off-road trail across North Carolina, and each year, as new trail opens, Friends adjusts the current route to incorporate that new trail. Over the last ten years, an average of 15 new miles of trail have opened each year. We expect that this rate of change is likely to continue in the foreseeable future." Therefore, the route is almost certainly has gotten "slower" over time.
"Pitchell" is a challenge dreamed up by Ashville, NC, runner Adam Hill, which is run on (mainly) a section of the MST, 67 miles from the top of Mt Pisgah to the summit of Mt Mitchell. See link for FKTs.