Hüsker Dü (try Zen Arcade first), My Bloody Valentine (their second album, Loveless is brilliant), Mission of Burma, Guided by Voices (Under the Bushes Under the Stars), Modest Mouse (The Lonesome Crowded West), the aforementioned Big Black, Pavement (start with Crooked Rain, Crooked Rain) and Neutral Milk Hotel (In the Aeroplane Over the Sea).
Also, Arcade Fire, Spoon, Okkervil River and Portishead.
Shit, did I mention Bedhead, listen to Bedhead (very slow indie rock), Pixies (anywhere is good) and Sleater-Kinney.
Oh, Polvo and Lungfish as well.
If you want to listen to Liars start with either last year's self-titled album or their first, They Threw Us in a Trench and Stuck a Monument On Top.