[peyton randolph]

Would they legally be able to do this even if Obama won the vote in their state? Has this ever come up before?

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Yes. There's been rogue electors in the past who have voted for the other candidate. Some states have laws that punish electors who do this...but such punishment would be after-the-fact, and there's some question as to whether these laws are even constitutional, i.e. whether the state has the power infringe upon the elector's powers.

[teletech]

My understanding of one of the reasons for electors is that they were to have final say because many Americans at the beginning of our nation weren’t educated enough to make good decisions. Sadly, that still applies. Perhaps the only reason the Electoral College is still around is the other reason, to balance small states vs. large ones. Electors can vote however they want, although they usually appear to echo their states’ majority vote.

Yes but doesn't the Secretary of State have to certify the election? If the electors go rogue, the SOS might just refuse to certify the election for that state.