As a foreign student under a practical training visa, what U.S. taxes am I responsible for paying?

Yes, you must file tax return if your income in 2007 exceeds $3400.
For nonresident tax filing requirements and other details, read Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents

You are responsible for income taxes (local, state and federal).

You are exempt from FICA (Social Security and Medicare) taxes.