I don't much hear jigs at jams or square dances, but they're alive and well at contras.
They're in 6/8, counted out as two groups of three per measure. An example I trot out to illustrate the rhythm to non-musicians is a nursery rhyme:
Humpty Dumpty sat on a wall,
Humpty-Dumpty had a great fall.
All the King's horses and all the King's men
Couldn't put Humpty together again.
On guitar, you can do this as a pair of boom-chucks per measure -- boom on the first beat, chuck for the third -- but a better approach is continuous strumming, one per beat, emphasizing the first strum of each measure. A single measure is DOWN-up-down, UP-down-up. It takes some getting used to. A thinner pick helps, and is a reminder to carry picks of different thicknesses.
On mando, I see some folks using this same technique, just alternating directions each beat, but that doesn't work as well for me as down-up-down, down-up-down. This makes, I hasten to add, no sense whatsoever.
Still, there you have it, in all its illogical glory.
Jigs give dance fiddlers the added challenge of how to launch into them; four potatoes -- ya-dada, ya-dada, ya-dada, ya-dada -- just ain't gonna cut it. Starting with the last two bars of the B is a good, musically, but can throw less-experienced callers, who've only ever started to four potatoes, for a loop. Joel Hayes handles it smoothly by telling the caller what he's about to do, then playing the intro a couple of times to get it in the caller's ears.
Sometimes, I play all-jig sets, but jig-to-reel sets, which start with a jig or two and then transition to a reel, are also fun because of the sharp contrast. Jigs are a lot faster than they seem, if you're playing them in isolation, and moving from a jig to a reel reminds you of this. You can be playing the jig at what seems like quite a modest clip, then transition to a reel and discover yourself struggling to keep up.
Reel-to-jig sets? Nope. Why? Not a clue.
A fine, traditional jig/reel pair is Garryowen with The Girl I Left Behind Me. For history buffs, the first was the regimental march of the 7th Cavalry, until they were wiped out at the Battle of Little Big Horn. After that, the tune was thought to be unlucky and was replaced by the second.