Which party controls the Senate if there is a 50-50 tie?
Article I, Section 3 of the Constitution specifies that The Vice President is the President of the Senate. The Vice President has no vote unless to break a tie in some matter before the Senate.
Therefore, if the election leads to a 50-50 party split in the Senate, the Vice-President's vote will give the majority to his or her party.
Since this is a presidential election year, an interesting event will occur if the Senate does end up tied after the 2012 election. Since the new Senate will be sworn in about 2 1/2 weeks before the new President and Vice-President (the latter pair take the oath of office on January 20th), the Democrats would technically be the majority party in that interim period. If the elected Vice-President is a Republican, the majority would then revert back to the Republicans after the 20th. This actually happened in 2001, with the two parties agreeing on a power-sharing arrangement during those interim weeks before George Bush and Dick Cheney were inaugurated.
A separate wrinkle in the 2012 race comes courtesy of the Maine Senate race, where Independent Angus King is well ahead of his party-affiliated challengers. Mr. King, the former two-term governor of Maine, has not indicated which party he will caucus with if elected, although he is a supporter of President Obama. If he wins, a tight battle for Senate majority could give Mr. King the power to decide which party will run the Senate in 2013.