I've done a lot of solo trips in the last year, starting with the UK parks most weekends, then venturing to Phantasialand and finally Disney World, Universal Studios and SeaWorld at the end of the year.
It can be daunting to start with and occasionally feel a bit odd, but I've had an incredible amount of fun on my own. There are some nice benefits, like you can just do what you feel like. Want to ride Nemesis or Duel for an hour? Then you can and no one will care and you won't feel like you're holding people up or dragging them onto things they're bored of. Although if you ride The Swarm 14 times in a day, chances are staff will recognise you - but they'll probably find it fun (and wish they were doing the same).
I've also found people can be quite chatty at theme parks. I've had a lot more random conversations whilst visiting on my own, than I've ever had when visiting with others. Staff also seem more likely to chat with you if you're on your own.
But as DeadJack5 says, if you go on the Shoutbox at the bottom of the main page, you may find that there are others at the park, or who are at home and are envious of your trip and will chat with you there. The TTSP events are also a good way of meeting people who you may bump into at the parks if you're there regularly.