If I had to pick a favorite band of all time, it would be Rush. ... 2112 was the first time I heard something where, lyrically, it didn't have to just be about the typical rock and roll topics, that it could be about something more heady or esoteric, something that makes you think. That really influenced me as a lyricist. I was also blown away by how a three-piece band could sound so majestic and huge and play in a style that's inherently rock and roll yet still pushes the boundaries of what they're doing musically-this idea of being experimental, using different time signatures and not really being concerned about song length and traditional constraints. I can't tell you how huge of an impact that had on me. 2112 basically set the course for my musical career and how I approached Dream Theater.
You can read the entire interview online here (thanks RushFanForever).