I'm another person who hiked alone a lot when I first became a frequent hiker simply because most of my friends didn't hike much. Within a few months I met many hiking partners through this site and the 3500 Club. Now I can often find partners pretty easily, but I also still really enjoy hiking alone, whatever we choose to call it. Pretty much for the reasons others have listed here.
I had a memorable experience last summer in the western Catskills. I bushwhacked a little place called Cradle Rock Ridge, then headed towards Beaver Meadow leanto. Some friends from my ADK chapter were doing trail maintenence that day and my intent was to do a little work that afternoon, then work w/ them all the next day. By the time I arrived at the leanto, I was kind of tired and very wet from wet brush. I wanted to rest and dry out a bit. The guys came back to the leanto in a short time and I apologized for not having got any work done, and said I was good for the whole next day. They said they were pretty much done, the trail had been in much better shape than they expected, and they didn't even need to bother spending the night, as they had planned.
They left after an hour or so, but I had schlepped in everything, so I figured I'd spend the night. The only problem-nothing to do! I'm one of those people who always has to have something to do. If I'm alone, I better have a guitar on which to practice, or a good book to read, movie to watch, something. Obviously I had nothing of the kind. I hadn't brought a book, since I figured I'd have leanto mates to chat with. So, after eating dinner and cleaning up camp, I just... sat there.
I ended up just sitting there for a good two hours doing absolutely nothing until I was tired enough to get in the bag. Fireflies filled Beaver Meadow as it got dark, and just about exactly at 9, coyotes starting yipping up on Millbrook Ridge-like they had punched the clock for the night shift or something! It was kind an interesting, repetitive rhythm they had happening. I realized sometimes it's really great to do nothing and just be. Sorry to get all Zen, but it really was pretty nice. That's what I think of when I think "solo."
Matt