I like way too much music to even begin with an encompassing list.
For music in 2009, I like: Animal Collective, Bat For Lashes, Pains of Being Pure At Heart, Phoenix, Neon Indian, Memory Tapes, Dirty Projectors, Twelves, Classixx, Fever Ray, Japandroids, Metric, Passion Pit, Yeah Yeah Yeahs, St Vincent, The XX... just to name a few.
From the past decade, I've liked: Interpol, Wilco, Arcade Fire, The Walkmen, Santogold, M83, Lily Allen, Ladyhawke, The Knife, Fleet Foxes, Cut Copy.
Some of my all-time favorites: The Beatles, Talking Heads, The Smiths, The Pixies, Sonic Youth, Sunny Day Real Estate.
I know I'm forgetting some real gems... oh well.