I recommend:
Muse - words just can't describe how amazing this band is. They're INCREDIBLE live; absolutely breathtaking. They've won countless awards for 'Best Live Act' because... carp, they blow you away.
If you're going to download or buy an album, get 'Black Holes & Revelations', 'Origin of Symmetry' and 'Absolution'.
I haven't made a topic about them yet because I have too much to say!
Porcupine Tree - A great rock band, their songs create a wonderful atmosphere and all of their albums offer something slightly different. They've got a slight Pink Floyd-ness about them, but the music is a lot heavier. Get the album 'Deadwing', I love it.
And for classical music lovers...
Alkan - anything performed by Jack Gibbons, preferrably. Alkan's music is sometimes beautiful, sometimes crazy, such as his 'Allegro Barbaro' -
http://www.youtube.com/watch?v=2dSqkzsWXlU (HARDCORE PIANO PLAYING BTW)
I think he almost faints after playing it, haha. Alkan is a wonderful virtuoso composer and Jack Gibbons a wonderful virtuoso pianist.
Chopin - typical, but one of my favourite composers. Listen to everything he has done. <3
J.S. Bach - He wrote tons and tons of music and I've only heard a bit, but his style is very recognizable and I think his music is wonderful. I love the English and French Suites and the Goldberg Variations. (surprise surprise)
Sergei Rachmaninov - Probably my overall favourite composer. Please listen to 'Piano Concerto No.3' if you haven't already - it's very well known and just amazing.