I've shown my gaited Paso Fino gelding in Trail, Halter, Easy-gaited Equitation, Easy-gaited Pleasure, gymkhana, jumping....only ever at fair, fun shows, and some smaller shows like 4-H
I've shown my one Thoroughbred in English pleasure and eq classes at the fair, and we're soon going to train for dressage. She's an excellent dressage horse.
Next year I'll show my other Thoroughbred in eventing.
I haven't shown any of the minis yet, but the two babies I will when they're a bit bigger.
My uncle has an arab and half-arab reining ranch in Colorado, and they have a ton of horses. 9 riding horses and a few 2-yr olds, plus 7 or so retired mares in the far pasture. When I go out to their ranch next I'm hoping to go to a show; their horses all go to nationals for Reining, Western Pleasure, Country English Pleasure, English Pleasure, etc. They mainly do reining, though. They show at arabian shows to earn points. I've ridden 8 of their 9 riding horses, and they're all spectacular. Their arab reining stallion and their English Pleasure National Show Horse (arab x Saddlebred cross in my avatar) are my favorites to ride.
Anyway, just a bit of the showing I do and hope to do :)