I've been a registered Republican for 27 years, ever since I first registered to vote in the 1980 presidential election. My initial decision was entirely tactical: I wanted to vote for John Anderson against Ronald Reagan in the Republican primary. Ever since then, it's largely been inertia that's kept me in the GOP, as I lacked any strong feeling of affiliation with either party, and with the closed primary system that had been effect in California until a decade ago, it seemed a form of self-disenfranchisement to not affiliate with one of the major parties. Now, however, with California's "modified closed primary", it seems reasonable to become unaffiliated with any party, as I can vote in the partisan primary of my choice (if the party allows). With that proviso, I can agree with KipEsquire that registering independent is an appropriate way to take a stand against the two party system.
As indicated in Kip's post, the open/closed primary issue is a bit of a mess. Here in California, we voters passed an initiative to have an "open primary" in 1996. That meant that voters could vote for any candidate in any party in the primary, regardless of their affiliation. In other words, if you're a Democrat, but the Democratic primary is not very competitive one year, you were welcome to vote in the Republican primary instead. Unfortunately, the US Supreme Court shot that down a few years later, holding that it violated the parties' freedom of association to be forced to allow non-members to vote in their primaries. In other states, however, closed primary systems, where only partisan-registered voters can vote in their party's primary, have also been shot down on association grounds. In particular, in Connecticut, the GOP wanted to allow independents to vote in their primary, but the state's closed primary system prevented that, and again the court held that the party's right of association was being violated. California currently has a "modified closed primary", in which each party gets to choose whether it will allow unaffiliated voters to vote their ballot. (Unlike the open primary, though, cross-over voting is still prohibited. The "modified closed primary" is only potentially a good deal for independents.) In the 2004 and 2006 elections, both the Dems and the GOP allowed independents to vote in their primaries. However, I just noticed that the filing deadline has passed for the upcoming presidential primary, and the GOP chose not to renew their invitation to independents. So it looks like only the Dems (and the American Independent party, in case anyone cares) will be open to California independents in February. I'm curious whether that was an intentional decision by the GOP, or they just missed the filing deadline. (The option needs to be explicity renewed for each election, 135 days in advance.) The Ron Paul forums are on top of this, but I didn't see any statement from the GOP. Plausible speculation is that party HQ is afraid if they let the independents vote the GOP ballot, too many of those votes would go to Ron Paul.
Personally, I liked the "open" or "blanket" primary that we had for a couple of election cycles, mostly because it was subversive of the two-party system. Constitutionally, I understand the freedom-of-association problem that the parties have with the open primary (as well as the strict closed one), and can even imagine a similar argument being made against the modified closed primary (i.e., what if a party wanted to allow its ballot to be offered to anyone, even if they were registered in a different party?). I think the fundamental problem is that if the parties are truly private associations, then why are public funds being spent to conduct "their" primary elections? Official elections are expensive affairs. If people want to form private associations to promote candidates, that's great, but why should taxpayers bear the cost of these associations conducting their private business of deciding who they want to promote? I say the constitutional solution to primary elections is to drop them altogether as a government-sponsored event. Or better yet, keep primaries as a chance to winnow the field, but keep it completely independent of the parties.
So, tomorrow I'll drop my registration in the mail officially declaring my independence from the party system. And look forward to the decreasing relevance of the D and R tags.