Don't look now, but in January, there could well be three independents in the US Senate, all of them caucusing with the Democrats.
We all know about Jumpin' Jim Jeffords, but two more are set to get in honestly. Vermont's Socialist (yes, really) Bernie Sanders is making the jump from the House to the Senate, and now Joe Lieberman is likely to be re-elected as an Independent, having been drummed out of his party. That would make three nominal independents, even though all three would effectively be liberal Democratic votes on social and tax policy.
Such a situation isn't unprecedented, although it is unusual, especially since 1900. (Searchable Senate database here.) In the mid 70s, Harry Byrd, Jr. of Virginia was an independent, and James Buckley of New York was elected on the Conservative line, but both caucused with the Republican minority. Further back, under FDR, there were four (or three) Senators who weren't official Democrats, but two of these were from Minnesota, whose Farm-Labor Party (later the DFL) was essentially part of the Democratic Party.
The DFL anomaly aside, independents seem most likely when one party seems firmly in control for a length of time, and party discipline on each side seems less important.