The tank burns up upon reentry. The tank stays with the Shuttle nearly all the way to orbit, as it must supply the fuel to the Shuttle main engines.
The tank's pretty light, when empty - I think it slows down pretty fast and doesn't completely burn.
Actually, I think I saw a video once 'way back during the earliest launches where they showed the boosters being recovered in the Atlantic and the tank/pieces splashing in the Indian.