I've honestly stopped listening to music almost entirely. But during the years I always had music on while I was awake, I easily liked progressive rock the most. It just kept my attention better than other genres, because it has lots of variation and creative ideas.
Some of my favorite bands are/were:
A.C.T, Beardfish, Discipline, Dream Theater, Echolyn, Genesis, IQ, Jethro Tull, Kansas, Karmakanic, Liquid Tension Experiment, Magenta, Muse, Opeth, Pain of Salvation, Porcupine Tree, Queen, Rush, Spock's Beard, Symphony X, The Beatles, The Flower Kings, Transatlantic, Yes and Änglagård.