The problem isn't as much voting either R or D, but that those are the only two choices. Both parties have a vested interest in making you believe that voting anything else is a wasted vote, since, by that logic, if you don't vote R, then D wins. This is only true if both R and D refuse to corporate with a hypothetical third party.
Multi-party politics can certainly work, and I would not want to limit the US to only 2 choices for the sake of it. However, multi-party setups where the number of separate parties get larger tend towards minority governments, coalitions with their own internal stresses, and generally less effective decision-making, with policy being driven by the need to keep a coalition together rather than "for the good of the people".
ok, I have probably just come fairly close to describing the current setup of the Republican party, which when viewed through the lens of long distance looks like several groups of escapees from the Insane Asylum, none of whom really like or trust each other, but who are driven by a greater dislike and distrust of "the enemy" (The Democrats). I suspect that there are equally deep divisions within the Democrat ranks, and these would be exposed during the campaigning process to choose a challenger to an incumbent President (by definition, the incumbent's lack of a need to compete against others within their party gives the appearance of unity).
Given things like the Tea Party agenda, their less-than-comfortable relationship with the GOP, and the underlying American/Republican frontier spirit which fuels a psyche of individual independence, governance and self-reliance, I suspect that a multi-party system would see 2 or 3 "Democrat" parties differentiated by non-core Democrat policies, and 3-8 "Republican" parties with variations of core Republican policies, plus perhaps independent parties organised along religious orientation lines.
That would have definite advantages - instead of an increasingly polarized argument between two behemoths, there might actually be genuine discussion of political and social matters less encumbered by rhetoric. Fundamentally though, you would probably find government being made up primarily of a Democrat coalition, with the Republican parties rendered largely ineffective by internal squabbling, leading to some of the more moderate Republican elements moving toward the center in an attempt to either differentiate and distance themselves from the playground name-calling or even trying to latch onto the Democrat machine.
In Europe certainly, multi-party politics tend to work fairly well, but generally with a relatively small number of discrete parties. I suspect that the US road to multi-partyism would explode into a larger number of small parties, which tends to be less effective, and in itself does not address concerns about competence or accountability of governments (Italy and Greece in recent history as examples).
Ultimately, I see the underlying problem being less that there are only 2 parties, but that those two parties fundamentally present as 2 ideologically opposed voices with no middle ground, but when looking at the detail behind the rhetoric, the two appear to be remarkably close together.