I listen to anything with nice rhythm and melody, rap is fine, only if the rap makes sense or it's not all gibberish rap from beginning to end, e.g where is the love by black eyed pea, one of the only rap songs that i don't find unbearable. I listen to mostly indie, alternative and rock.
Rilo Kiley, Coldplay, Voxtrot, The Cab, Boys Like Girls, Corrinne May (slow ambient pop, good for insomniacs, I love this album when I feel sleepy but can't sleep), The Strokes, Within Temptation, Imogen Heap, Fiest, Paramore, Train, This Providence, Stars, Skillet, Relient K, advantage Lucy, BoA, xoxo Panda (korean indie) etc.