I know Georgia gave Andrew Jackson 100% of the vote in 1832. I don't know how that could have occured, but it actually did.
There were actually two slates of electors representing different factions of the Democratic party. The slate supporting Jackson and Van Buren received 13,881 votes; the slate supporting Jackson and Phillip Barbour of Virginia received 7,367 votes. There were also Jackson/Barbour slates in Alabama, Mississippi, North Carolina, and Virginia. In some of these states there was also a Clay slate (this was before the advent of the papyrus ballot), but in some it finished 3rd behind the two Jackson slates.