I started to go to conventions about 12 years ago. I only wish I had started 15 years before that. I have met a lot of great people and had a lot fun. I don't get to go to very many cons, but here are some I have been to and enjoyed. You can check out Jenga's Conventions website for information on cons near you.
I really like going to SF & Fantasy conventions. Some emphasis the written word, others are more concerned with films and television. But they have all had interesting people and good times.
The first SF con I attended was Balticon. Unfortunately for me, Balticon is now held over Memorial Day weekend either in or near Baltimore, MD. Since Marcon has also moved to Memorial Day weekend, (Actually, Marcon was there first, by a year) I can only attend one of them.
Here in Ohio I attend Marcon every year. It is held every year on Memorial Day Weekend in Columbus, Ohio. Much more media oriented than Balticon, with 24 hour anime and movie rooms. But they also have great author GOHs. 
The World Science Fiction Society has a site with information on all of the upcoming Worldcons. You can check out who is in the running for upcoming Worldcons on this bid page.
LA Con III was a lot of fun. Both the Masquerade and the Hugo ceremony were worth seeing. There were also some really good panels and a very good dealer's room. Unfortunately I spent entirely too much money in the latter. Good thing I had cancelled out of the gaming cons.
LonestarCon 2, the 1997 Worldcon, was held in San Antonio, Texas. It was lots of fun. I met many people for the first time that I have known for several years online. And I met some very nice people that I had never met before. Well worth the time and money.
BucConeer, the 1998 Worldcon in Baltimore, MD, was lots of fun, got so see some friends and once again spent far too much money.
Aussiecon 3, the 1999 Worldcon in Melbourne, Australia is something I am really looking forward too. The con was from September 2 to the 6th and I spent more time before and after sightseeing. My pictures of my trip are online at my Travel Site.
Conucopia was the 1999 Nasfic held in Anaheim the weekend before Aussiecon.
Chicon 2000 was finally be a fairly easy Worldcon for me to get to. Only a 4 hour drive, or it would have been if I had not went by way of Mt. Rushmore. Unfortunately, my camera shutter died, so I didn't get the pictures I thought I was taking. Which means I have to go back to the Badlands. Such a sacrifice.
The Millenium Philcon in 2001 was a fun time. I got there by way of Massachusetts, Vermont, and New Hampshire. I didn't get to do any real sightseeing or have a real Philly Cheesesteak sandwich. Somewhere else I will have to visit again.
ConJose was the 2002 worldcon. I had to cancel my trip due to the death of a close friend.
Torcon III was held over Labor Day, 2003. It was disorganized, and some people had several problems, but it was a very enjoyable convention for me.
Noreascon Four will be held in Boston in 2004. I would have liked a trip to Charlotte, but Boston and the New England area will be fun too.
Interaction will be held in Glasgow in early August, 2005. A chance to spend a couple of weeks wandering around the British Isles. Assuming I can bring my self to leave the British Museum. 
L. A. Con IV will be the site for the 2006 worldcon.
Columbus in 2007 is taking on Nippon2007 for the WorldCon, and it should be an interesting fight.
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