I pretty much just think, "Oh, this person stutters," and go on with the conversation. I certainly wouldn't have any urge to laugh because I don't see a thing funny about a person's "challenge" (if that's the right word). I don't particularly feel sympathy because I know that something like that is no indication of how intelligent, strong, weak, etc. anyone is; so I see no reason to sympathize. Sympathy suggests feeling bad for someone, and a) I respect the other person enough not to think they're "less" because of their problem, and b) the person probably learned long ago how to comfortably get through life while having that kind of "challenge".
Is it always easy and effortless to listen to someone who has that particular challenge? No, but there are a lot of things/people in life we have to listen to/hear that aren't all that effortless.
My thinking is this: I do with that what I do with, say, a person who has a very thick foreign accent - I hope they feel fine about it and know I don't have a problem with it either, have no impatience or problem whatsoever with understanding that it may take them a little more time/effort to say what they need to say; but also hope the other person understands that if I can't understand something he has said neither of us should feel bad about that either and should just do our best to work with it.