He became a beef and chicken importer/exporter in Shreveport, Louisiana.
OK, no… he didn't do THAT, but the only answer we can say with any degree of certainty is he left Twin Peaks to "see the world." And why wouldn't he? For pete's sake, look at what happened to him: In the span of less than one month (of "real time" in the show's chronology):
(SPOILERS) His girlfriend died, he fell in love with the best friend of his dead girlfriend, he started falling for the semi-identical cousin of his dead girlfriend… a cousin who was then murdered by the same man who killed his girlfriend (who was then identified as his girlfriend's father). Oh, and after all this he gets entangled with a woman who wants to have him kill her husband and almost goes to jail over it! I know high school is a dramatic time for many, but come on!
If I was James, I'd have done exactly what he did – hop on his bike and get the hell out of that town. And I'd have done it a lot sooner than he did.
The real answer as to what happened to James Hurley? Writer/producer Mark Frost ran out of plot for his character, and he was written out of the show.