In this decade:
I love the new album by Neko Case, Middle Cyclone. Thought it built on the promise of Confessions. If you like pure female vocals, I can highly recommend Cat Power, Keren Ann, Maria Taylor, Shelby Lynne, Lucinda Williams and Jenny Lewis.
I really loved the flamengo stylings of Rodrigo & Gabriela.
Their take on acoustic metal witha Latin flair was brilliant.
I liked the roots rock feel of Calexico, Dave Alvin and M. Ward.
From England, I loved M.I.A. and Lily Allen. Original takes on global music and witty lyrics. For bands, I loved Elbow (sounds like vintage Peter Gabriel), Radiohead, Coldplay and Muse.
Brooklyn spawned dozens of great bands. Grizzly Bear, MGMT, TV on the Radio, Santogold, Yeah Yeah Yeahs and Vampire Weekend stood apart and made some of the most thoughtful and clever Indie music this decade.
Here in So Cal, where I reside, we had some amazing bands as well, including Beck (Seachanges!), the Cold War Kids (Cowards and Robbers!), the Eels, the Submarines and the Silversun Pickups.