When I was on my CP, I'd go to the parks by myself all the time. If nobody was around to hang out with, I'd just head over to one of the parks and enjoy the atmosphere. Sometimes I wouldn't even ride a single ride. I'd just walk around taking pictures and discovering new things. I also had a reunion trip with some co-workers, but they could only come down for 4 days, and I thought it was silly to pay that much for a flight and only stay for a few days, so I flew down 3 days before my friends and got my own room. I had an awesome time by myself, but I'm a natural loner anyway. When I first started going on rides by myself, I felt awkward saying I was a single rider all the time, but then I remembered that I didn't even give single riders a second thought when I was working. The best part, like others have already said, was getting to do whatever I wanted whenever I wanted to do it. If I wanted to ride one ride, and then hike all the way across the park to ride something else, there was nobody to complain about too much walking. If I wasn't hungry, there was nobody to try to coordinate my stomach with. I could stay for every last second of EMH if I wanted.
If you don't mind being alone, or if you're relatively independent and you like exploring things on your own, you'll have a great time no matter what. I think Disney is 90% attitude anyway. If you come there determined to have a good time, you will, whether you're by yourself or with a party of 15. If you come down there expecting everything to be boring or lame, that's exactly the kind of vacation you'll end up with.