/run CallCompanion("CRITTER", random(GetNumCompanions("CRITTER")))
As you've probably surmised, it'll choose a random critter from your noncombat pets and bring it out for you to play with. As I said, this is super-simple -- you could add /dismount on to the front of this and use it as a one-stop "dismount and summon pet" macro, or I'm sure our commenters (who are much better at this macro stuff than I am) will have lots of other ways to play. We posted a more complicated one a while back, and you can still replace CRITTER with MOUNT, but this one's even easier than that.
But like Bornakk, I tend to collect way too many noncombat pets and I can never choose which is my favorite. A random macro like this helps pull out a friend I haven't seen lately.