My favorite band, bar none, is Rush.
I do also like Foxy Shazam (though no one knows who they are... yet), System of a Down, Daft Punk, The Flaming Lips, Nine Inch Nails, Yoko Kanno... and a lot more. I do like some power/speed metal, but I've started to kind of grow bored of it as it all seems to sound the same. The stuff I like tends to be multi-layered, though this isn't always the case. But I don't get tired of complex music nearly as quickly as other stuff.