Mark Twain wrote a short piece about his Civil War experience. The second paragraph is an amusing example of side-switching.

Out west there was a good deal of confusion in men's minds during the first months of the great trouble, a good deal of unsettledness, of leaning first this way then that, and then the other way. It was hard for us to get our bearings. I call to mind an example of this. I was piloting on the Mississippi when the news came that South Carolina had gone out of the Union on the 20th of December, 1860. My pilot mate was a New Yorker. He was strong for the Union; so was I. But he would not listen to me with any patience, my loyalty was smirched, to his eye, because my father had owned slaves. I said in palliation of this dark fact that I had heard my father say, some years before he died, that slavery was a great wrong and he would free the solitary Negro he then owned if he could think it right to give away the property of the family when he was so straitened in means. My mate retorted that a mere impulse was nothing, anyone could pretend to a good impulse, and went on decrying my Unionism and libelling my ancestry. A month later the secession atmosphere had considerably thickened on the Lower Mississippi and I became a rebel; so did he. We were together in New Orleans the 26th of January, when Louisiana went out of the Union. He did his fair share of the rebel shouting but was opposed to letting me do mine. He said I came of bad stock, of a father who had been willing to set slaves free. In the following summer he was piloting a Union gunboat and shouting for the Union again and I was in the Confederate army. I held his note for some borrowed money. He was one of the most upright men I ever knew but he repudiated that note without hesitation because I was a rebel and the son of a man who owned slaves.

Though Twain's account is obviously dramatized, it does describe some of the ambivalence of the early days in a contested state like Missouri - even a Union sympathizer might not take kindly to his state being invaded by Federal troops.

I can think of at least one example. Henry Morton Stanley, who later found British explorer David Livingstone, joined the Confederate Army and then switched to the Union Army after being captured at the Battle of Shiloh.

I'm not sure how common this was or if it really answers your question since I doubt the switch was 100% voluntary. Mods, I'm no expert so feel free to remove my post if it doesn't meet the standards of this sub.

It happened on both sides. I think the term used for Confederate POWs who switched was "Galvanized Yankees'.

Here's a link.

the most well known officer to switch is probably Frank Armstrong who led a union cav. company at 1st bull run then became a confederate general. The article also references a Joseph Sanders who switched the other direction.

http://en.wikipedia.org/wiki/Frank_Crawford_Armstrong

I do not know of any other officers who switched.

EDIT: you could also add confederate general Kirby Smith, who was fairly well known. WHen the war began he was in Texas and refused to surrender Ft. Colorado; Jan '; 61. By march, he was in confederate service. So although he did no fighting he was in union service.