The first song I listened to fully by Dream Theater, was The Glass Prison. My friend had actually been getting me into a lot of thrash, power and other kinds of metal when he lent me Six Degrees, IaW and Systematic Chaos. Of course, being into more of the metal oriented stuff I loved tgp, and started to enjoy a lot of songs from SC. But, I didn't like James Labrie a whole lot at first, like other people have already posted.
Then I was at best buy with a gift card and I decided to get a live DVD, I was looking through slayer, megadeth, etc. when I saw Chaos in Motion. I wasnt a huge fan at this point still but I wanted to try to get into them more, so I got it, and didnt really watch it fully (didnt have the musical patience yet) and of course picked out a few songs that I liked and watched them over and over. I liked the DVD, so I went out and bought Score, and watched it all the way through. I've been a hardcore fan ever since, and learned to appreciate JLB.