What kind of bit people are using for jumping?

It looks like you are riding with just a gag rein in your avatar. I have no problem with gags. So much better that twisted, wire, waterfords...etc, IMHO.

i tend to use an typical jointed eggbutt- on my young horse i have a rather thick/angled hollow eggbutt- but for poor Tangles he has a rubber pelham- which is practically all i can ride him in coz the old owners destroyed his mouth with all types of gags and ties and whatnot-- but i'm slowly bringing him back to an ordinary loose ring snaffle

yep, back then i did cos he was new and i wasn't ready to ride xc with double reins.
i think they're fine if they're used in the right hands. :)

double jointed lose ring for everything

yay, charli was in a pelham and now I have him in the double link, its so worth it =]

I jump Fiona in a full cheek single jointed happy mouth snaffle at home and a happy mouth single jointed pelham at shows because she gets a little hyped up.
With Bru I'm still figuring things out as he's slowly coming back from lameness. I use to ride him in a kimberwicke for jumping (single jointed) as he gets quite strong and heavy but we're working on that, been riding him in a rubber single jointed full cheek.
With Fiona (never tried Bru with one) she disliked a french link, I think due to her small mouth. And actually she really really like a curb bit, I think the pressure makes it easier for here to understand but who knows.

The hunter bit around here is full cheek or D ring, and D ring I think has always been the cheekpiece of choice with all the big names riding in it, though full cheek is coming up.

i use a full cheek kinmberwick

at home i use a slow twist egg but snaffle (we are just doing little jumps :) )

at shows i use either the above or a full check french link

Are there any limitations on WHAT bit you can use at the show? Like in dressage you can only use this and that.

In dressage you can only use snaffles in the lower levels . In showjumping over here you can use any bit as long as the judge sees that the rider is using it property