Ah, Dream Theater. I've been a fan for a while. They're a progressive metal band, and a brilliant one at that. They may have some weak composition at times (their new album, Train of Thought that just came out, for instance)--but, they feature some of the most brilliant musicians: John Petrucci (guitar), Mike Portnoy (drums), John Myung (bass)--and ill-fabled James LaBrie. I'd reccoment checking out songs from Scenes From a Memory, as well as Images and Words. Though, some of my favourite songs include...
The Glass Prison
The Great Debate
Home
Six Degrees of Inner Turbulence (all 8 parts--42 minutes of bliss!)
Blind Faith
This Dying Soul
...And some others, which I commonly forget.
You also may want to try some of their side-projects, especially Liquid Tension Experiment (a fully-instrumental band), with these songs:
Acid Rain
When The Water Breaks
Biaxident
Another Dimension
EDIT: AND IT'S DREAM THEATER!