With 96% of Georgia’s precincts reporting, the U.S. Senate results are: Chambliss (R) 49.9%, Martin (D) 46.7%, Buckley (Libt.) 3.4%. Georgia is the only state in which no one can be deemed elected to the U.S. Senate without 50% of the vote. It seems somewhat likely the state will need a runoff in December, although this is far from certain. See this article. Thanks to David Gillespie for the link.
For statewide constitutional offices, Mississippi requires that a candidate (1) get 50%-plus of the vote, and (2) carry a majority of the 122 state House districts. If both criteria are not met, the state House chooses between the top two vote-getters in January.
It’s worth noting that, when no candidate for governor of Vermont gets 50%-plus of the popular vote, the governor is elected by a joint session of both houses of the legislature.
I had first thought that, in Washington state’s “top two” for state and congressional offices, 50%-plus is required to win. But then I remembered that Washington allows write-in votes in the final election.