I would make the case that polarization is a good thing. Polarization means you know, as a citizen, how to translate political activity--voting, volunteering, donating--into policy results. If every Democrat is to the left of every Republican on some issue, then if you want to move the status quo to the left you support Democratic candidates but if you want to move it to the right you support Republicans.
This is a subject near and dear to my heart, since this time last year I was locked in a library struggling in vain to write a coherent senior thesis on this topic. The phenomenon Matt calls "polarization"--the sorting of left-of-center people into the Democratic Party and right-of-center people into the GOP--is referred to by political scientists, logically enough, as "sorting." For the reasons Matt cites, this is widely considered to be a good thing, as throughout the '50s and '60s political scientists were constantly urging the parties to be more ideologically cohesive. What political scientists term "polarization"--a shift in the distribution of the public's ideological views away from the center of the spectrum and toward the extremes--has not occurred, as Morris Fiorina, among others, has shown. The underlying distribution of ideological views has remained more or less constant over the past forty years.
So far, so good. The problem is that the sorting has been accompanied, particularly in the past two decades, by an increase in a third variable, which might be termed "partisanship." Partisanship primarily concerns not ideology but process and temperament: more partisan individuals are more likely to believe that the best way to implement one's policy preferences is to shun bipartisan cooperation, unify one's base, opt for confrontation at the ballot box, and try to push through an agenda with fifty-percent-plus-one support. Of course, this is simply a legislative strategy and is neither inherently "good" nor "bad." But in a system that, despite what Matt might wish, effectively contains a supermajority requirement for any major policy change (not to beat a dead horse), it's usually not going to be a very successful strategy. And because it sows distrust between the two parties, it makes it harder to get anything done even when there's the possibility for bipartisan agreement. There's a widespread belief, for instance, that the tax code is fundamentally flawed in various ways, but because of the prevailing political culture in Washington, it's hard to envision a reprise of the 1986 Tax Reform Act.
In my opinion, one of the more interesting questions in American politics is whether one can have sorting (which is good) without partisanship (which is, for the most part, not). The two are not, at least in theory, mutually inclusive: one can easily be an unabashed liberal or conservative while still recognizing the necessity of bipartisan cooperation (Ted Kennedy being a prime example). I'm cautiously optimistic on this front: we don't have much experience with a sorted system, and eventually people are bound to realize that the Rove–Krugman theory of politics doesn't really get you anywhere. But only time will tell.