Perhaps the two most important components of fishing are, first, the hook set and second, getting the sharp thing back out.
Many times hook removal is accomplished by hand especially when using the catch-and-release friendly circle hook or a single, visible standard hook, connected close to the edge of fish’s mouth. For example, tournament bass anglers fishing a jig with a large single hook have a nifty way to dislodge the hook by turning the jig to an exact position and then giving the top of the jig a quick, firm pop with the palm of the hand. However, when dealing with an unfortunately deep hook or a set of treble hooks and a particularly feisty fish, a handy removal tool can prevent further damage to the fish and/or your hand. (The smaller fish can be the most dangerous to handle.)
The bluntly named fishhook “disgorger” frequently accompanies fishing tackle starter kits. Plastic, inexpensive, and easy to use, this device comes in handy especially when using live bait and the hook set was a little late.
There are several other tools for this task. The squeeze out hook remover is getting some great reviews and the stainless steel hook remover is frequently spied on boats, especially in the North where toothy fish like pike and walleye lurk.
Fly anglers generally prefer to carry surgical forceps. Not because you have to be a medical doctor to afford fly-fishing, but because these precise tools are ideal for removing a dainty, miniscule fly from trout.
I’m a long-nosed pliers guy. I’ve got the holes in my back pockets to prove it. This tool is not just practical for reaching a hook in the back of a tiny-mouthed bluegill. It also helps cut line, pinch on split-shot, and increasingly, crimp down the barbs on my hooks.