The 20th Century, particularly the latter half, was one of dominance of the Congress by the Democratic Party.
After swapping control around in the first part of the century, the Democrats roared into power in the 1932 elections, taking the presidency, the House and the Senate.
They lost the House in 1946, took it back in 1948, lost it again in 1952 due to Ike’s coattails, retook it in 1954 and held it for the next 40 years. They held the Senate for most of the history between 1932 and 1994 as well, with small bursts of Republican control in 1952 and during the early 1980s.
In 1994, a realigning election, in which the GOP perfectly played a hand that included great skepticism of the Clinton healthcare plan, the GOP took both the House and Senate. Though their margins narrowed election over election (aside from 2002, when the GOP gained in both chambers), they have held it for the next ten years (mostly… see below).
Why did the GOP hold the House? Because Clinton had no coattails. The margin of GOP control in 1995-1997 was so slim that a more successful reelection bid by Clinton, who didn’t get a majority of the popular vote in 1996, would have been sufficient to take back the Congress. However, that didn’t happen, though the Democrats came close to taking back the Senate in the late 1990s.
In 2000, the Senate split 50-50, giving the GOP organizational and effective control due to the fact that GOP Veep Dick Cheney was the tie vote. But then Jim Jeffords switched sides, throwing control back to the Democrats until January 2003.
Right now, trends work against the Democrats making a sweeping return to power in the House this year. We’ll see if they continue to erode the GOP’s majority, which was down to practically nothing before the 2002 midterm elections. If that is the case, then they could conceivably retake the House by the end of the decade. In the Senate, chances for the Democrats are better.
Regardless, one can expect battles for congressional control to be fairly close and very hard fought for the foreseeable future.