I suppose I never really thought about it. They have jaws on the sides that move laterally in and out and a labium and labrum (sort of like rigid upper and lower lips) that are hinged at the base and move a bit; also there are palpi (short antenna-like appendages) on either side that can move freely and seem to be sensory, perhaps used to taste. But as far as "baring teeth" in an aggressive display, I haven't really noticed that with most grasshoppers; I suppose that's just sort of the everyday look for a grasshopper.

When you are holding them (and after they settle down and decide to stay for a while), they will often walk around and lightly touch and nibble at your clothing or skin, but I don't think that has anything to do with agression or defense. Occasionally (it's pretty rare) they will try to bite when you first grab them, but it's a pretty meager attempt, and I've never had one that could bite hard enough to even really notice. However, some kinds have been known to eat one another when confined in a jar together.

Some grasshoppers do behave agressively in defense, but they tend to use their legs and wings for any sort of display, and some species will rear up, lunge at you, ooze (apparently nasty) liquid, and/or hiss. However, I haven't really noticed them using their mouths in any sort of display, and I need to pay more attention.

As for Band-wing Grasshoppers like this one, they don't really seem to be agressive at all. They just try to get away, and if you grab them they spit. If they get used to being held they sometimes do the surface tasting thing.

On the other hand (this is a bit generic, but generally true) most Katydids and their closer relatives will agressively bite, and some of them can easily draw blood. A few would be quite happy to start eating you if you held onto them long enough.

As for crickets, I've been bitten when holding them, but only a couple of the biggest species can make much of an impression. Mostly they are cowards of the utmost degree, and just run away.

And so on - lots of insects are biters, most are not. Some put on quite a show, sometimes with their mouths, most do not.