A lot of laughing shots are candid - the photographer just happened to catch them at the right moment. But, there are ways of getting people to laugh, too.
Getting them to relax is key. If photographing more than one person (either a couple or a group), get one of the people to tell a funny story involving at least one, or even all of them - they're more likely to laugh at something like that, than something you'd say.
When photographing young kids, potty talk works wonders! I made a bunch of kids crack up by yelling out "monkeyfarts!" right before I took the shot.
This is one that I took by using potty talk. She was laying on the ground, as serious as could be, and I got some nice serious shots - but then I just started saying the silliest things and got this:
For teens, I'll say something like, "Pretend I'm not a complete dork and that you like me at least a little, would ya?" Not so much of a roaring laugh, but usually at least a snicker.
I'm sure lots of other folks will have more suggestions!