I don't think I've ever really changed my mind on a very serious issue. There have been times where I've become more willing to see both sides or become less dismissive of the other viewpoint, but most of the time, I tend to stick with my general beliefs without any radical changes.
I have changed my mind in that I've not pursued things that were once very important to me. After years of frustration and delays, I gave up on things that were once very important goals; it seemed the only logical thing to do. It wasn't so much abandoning a point of view so much as realizing that a certain goal was just never going to be reached.