Yes! If you are a U.S. citizen living abroad, at least 18 years old on the date of the election, and eligible to register to vote in your state, then federal law guarantees your right to vote in federal elections - for President, U.S. Senate and U.S. House of Representatives.
And every state allows at least some citizens living abroad to vote in state and local elections (for governor, state legislature, mayor, etc.). See also FAQ #3 (“Can I Vote In State And Local Elections?”)
VoteFromAbroad (VFA) will assist you in filling out and submitting your Federal Post Card Application (FPCA) to your Local Election Official in the U.S. After your FPCA is accepted, you will receive a ballot covering every race in which you are eligible to vote for the remainder of the calendar year.