If you filed federal taxes in the U.S. chances are you will need to file them when abroad.
You may also be required to file a U.S. state tax return when abroad.
If you are a U.S. citizen, or green card holder, with money in a foreign bank account, you may also need to file an FBAR (Report of Foreign Bank and Financial Accounts).
If you own a foreign corporation, mutual funds, etc., you may have to file additional information return.