Is there any reason to vote against the predominant majority?

Let us take the example of voting in a U.S. presidential election. If one lives in a blue state for which the outcome of the vote is known to always favor the Democratic candidate, is there any reason that would prompt one to vote Republican, or vice versa?

I have always heard the argument that for Republicans in, say California or Massachusetts, it is essentially pointless to bother voting at all. The same would apply to Democrats in Tennessee or Oklahoma. Is there a counter-argument to this claim?