With Minnesota's Al Franken taking a seat in the U.S. Senate, Democrats in that chamber potentially control 60 votes -- the number needed to overcome a Republican filibuster. That majority is comprised of 58 Democrats and two independents, Joseph Leiberman and Bernard Sanders.
The Senate web site provides a handy reference describing the party composition of the Senate for every Congress going back to the first (1789-1791). Each entry has the numerical breakdown, plus notes on any special circumstances (such as members dying or switching parties).
Here's a question for history buffs: when was the last time one of the parties held at least 60 seats in the Senate? Answer: the 95th Congress (1977-1979) when the Democrats had 61 (with 38 Republicans and one independent, Harry F. Byrd Jr., who voted with the Democratic caucus).
Incidentally, there's also a page showing the party division in the U.S. House (1789-present).