I've been to anime conventions. I went to A-Kon (Dallas, TX) twice and I've been to MechaCon (New Orleans, LA) once. They were all pretty fun. I'm not quite as into anime as the friends I went with, but I had a really good time just looking at all the cool stuff for sale, dressing up, and going to the various dances and other functions. I saw a great Rocky Horror midnight showing at A-Kon one year! It was a great excuse to go somewhere fun, get a hotel room, and spend a weekend with good friends that I hadn't seen in a while.
I'm not sure if "purists" would consider it a convention, but I did go to Star Wars Weekends at MGM Studios a couple of times. (I absolutely refuse to call it Hollywood Studios!) People came in costume, they had cast and crew members doing meet & greets and autograph sessions, interviews, special events, etc. So yeah, I would consider it one.
Also, when I was about seven or eight, I went with an uncle of mine to a ham radio convention. I don't remember much about it, though.
I've been to Anime Expo and a con in Sacramento but I haven't been to one in YEARS. I loved it but I want to go to one when I can cosplay and go everyday. Each time I've been to a con I only went one day.
I've been to political conventions and conventions for work. I find them extremely tiresome. I'm not terribly social to begin with, and the constant happy horseshit of introducing and selling yourself just makes me want to run away to the wilderness for a month.
I think an adult convention (like AVN) could be fun. Or any convention where I don't have to 'work the room', really.