Oregon and Washington vote entirely by postal mail. The Oregon Secretary of State, Kate Brown, recently told the U.S. Postal Service that if a voter sends in a ballot without enough postage, Oregon law requires that the post office not deliver that ballot to the elections office. The Postal Service responded with this October 31 letter. The Postal Service says the Postal Service is not bound by state election law and that the Postal Service will continue its policy of delivering ballots to election offices, even if the ballot arrives “postage due.” Presumably the motive of the Oregon Secretary of State is to save election administration costs.
In Oregon, ballots must arrive by the end of the day on election day, which is November 6 this year. Thanks to Dan Meek for the link. UPDATE: even though the postal service delivers these ballots, some Oregon counties are refusing to count ballots that arrive with postage due.