Democrats have been projected to win the governor's races in the U.S. states of Virginia and New Jersey.
In Virginia, preliminary results show Lieutenant-Governor Tim Kaine defeated Republican Jerry Kilgore by five percentage points.
Preliminary returns also show Democratic Senator Jon Corzine with a slim lead over Republican multi-millionaire Doug Forrester in New Jersey.
Analysts were watching those two races to see whether President Bush's low approval ratings would hurt the Republican candidates at the polls.
In Texas, voters overwhelmingly approved a state constitutional ban on homosexual marriage.
Elsewhere, voters elected mayors in several cities, most notably New York City, where Republican incumbent Michael Bloomberg was projected to easily win re-election.