Well, the short answer would be, only when we find something funny.
'Do aspies laugh' was one of the search terms used to find my blog recently. I imagine the person searching was confused by their aspie's stony-faced reaction to something mega-hilarious and obviously irresistible. Or perhaps the aspie said the hilarious something was funny, but then didn't laugh?
It must be confusing to people, in a world of comedy, when a person doesn't laugh. Laughing at funnies is a great big part of people-pleasing, even if the only people nearby are the ones in the cinema audience.
Showing you share the joke also shows you understand the joke and understanding and sharing the joke means you also share and understand your fellow humans. To not laugh at something everyone else seems to find funny sets you apart and tickles some instinct in others, that you are not the same and might be untrustworthy.
I've had the joke explained to me before now, in great detail. It's as if the absence of it being funny makes people try all the harder to explain why you are in error. Here, it is funny because of this, do you see? Or, this was the funny part, do you see it now? And then they wait for you to laugh.
At this point, even if it was amazingly funny, most aspies wouldn't laugh because by then we have an audience - a really keen audience, watching us closely, waiting for what passes as an emotional reaction. There's nothing like an avid void, waiting to be filled with emotion, to put an aspie off their game.
Okay, so you don't have to laugh when you find something funny. I suppose you have to do more than make a weak-willed smile though. And definitely more than stand for a moment, study the situation and then go back to what you were doing without a glimmer of amusement.
Yes, aspies do laugh, at things that are funny. And very often at things that are not. And myself and RT Teen are the kind of aspies who laugh before the joke is told, or before it has started to happen, because we see it coming and fill in the rest. We find it equally incomprehensible that people wonder what we're laughing at - it's funny, isn't it? Didn't you see it coming?
Aspies do not laugh to make other people feel better about finding something funny. They do not laugh because everyone else is laughing (are more inclined to find the laughter of others distracting). Aspies do not laugh to show they are part of the great human condition. They laugh only if they find something funny enough to warrant laughter. Or at inappropriate moments in public places. Or at an internal joke no one else can see or hear.
If your aspie is not laughing when you expect, do consider the possibility you aren't hitting the right mark and try again. Sooner or later you will both find the same thing funny. Until then, don't worry about it. There's more to life and love than laughing at the expected and much more to humour than a face cracked wide in a smile.