As 2009 came to a close, it seemed clear that the Democrats would suffer some net loss of Senate seats in the 2010 midterm elections. The question was whether those losses would be minor, or would significantly cut into the Democrats' majority. Then, Democratic incumbents in North Dakota and Indiana announced unexpected retirements. And, of course, a Republican won the Massachusetts special election. Now, a significantly reduced majority looks like a best-case scenario for the Democrats, and the talk is about whether the Republicans can return to majority status.
There are currently 41 Republicans in the Senate. A net gain of 10 seats would restore the Republican majority that was lost at the 2006 midterms. They need 51; a 50-50 tie would be resolved in favor of the Democrats by Vice President Joe Biden who, as president of the Senate, is granted a tie-breaking vote by the Constitution.
Gains of 10 seats or more are rare, but not unprecedented. Here is a link to historical statistics on party division in the Senate, from the Senate website. During the 20th century, parties made double-digit gains in the following years:
1980 Republicans gained 12 seats
1958 Democrats gained 16 seats
1946 Republicans gained 13 seats
1942 Republicans gained 10 seats
1934 Democrats gained 10 seats
1932 Democrats gained 12 seats
1920 Republicans gained 10 seats
1910 Democrats gained 12 seats
These numbers might be somewhat distorted, because they don't take into account 1) results of special elections or party-jumping since the previous general election, 2) senators who were elected on third-party tickets, but caucused with a major party; and 3) the effect of new states joining the union. But they give some sense of the rarity of such an event: eight times out of 50 biennial elections.
Next, I'll look at the individual states in which this question will be decided.