As much as I try not to be upset, bigoted jokes do bother me, even if I'm not the intended target. For one thing, I have no desire to associate with bigots. I've encountered far too many people who use the fact that their vitriol is in the form of a "joke" as either a cover or an excuse for its vileness. I don't think it's political correctness to be repulsed by thinly-veiled bullying, but basic human decency. That I can empathize with the targets precludes me from finding said "jokes" funny. That being said, there is a difference between mocking the absurdity of a stereotype and earnestly using stereotypes to mock. The former is ok, the latter is not. Dark humor is also something different (and I have a dark sense of humor) from bigoted jokes.
Alas, I am guilty of not correcting offenders nearly as much as I should. My reaction tends to be facepalm followed by avoiding/disassociating from them rather than calling them out on it. If it's someone I know does it, I may say "dude, not cool," but with strangers I usually just walk away. As much as society would benefit from censuring its predators, I seldom do it myself. For one, there is that fear that if I speak up, I'll be next (as Beth Andrea mentioned), but also the fact that some idiots just aren't worth one's time. I just don't need the stress.