Explain the benefits and drawbacks of casting your vote for a presidential candidate from a minor party?

As someone who has voted for a third party candidate twice, I did so because I didn't like either the Republican or Democratic candidate and I wanted to cast my vote for someone I could believe in. I do not regret either of those votes, even though I knew the third party candidate could not win. I'd rather support the losing side when it's right than the winning side when it's wrong.