1) Tactical: to prevent people from knowing that you are firing nearby, or at least to cloak your location while you are firing if you are using supersonic ammo (such as with a normal sniper rifle)
2) Noise Control: your neighbors don't like it when you fire your machinegun at 3am. This might not seem like a good reason to you, but in countries where suppressors are legal (Norway? Finland? It's one of those countries up there) it's as good a reason as any to use one. Why bother using ear protection when you can just slap on a suppressor?
3) Controlling muzzle blast: when agents raid meth labs, they don't want the whole place going up in flames because their muzzle blast interacted with some flammable chemicals
4) Fire control: suppressors can result in less jarring recoil. They generally work by slowing the rate at which the gas leaves the barrel (it's the supersonic movement of the gas that makes most of the firearm's noise). In doing so, they increase the time the recoil is felt, making it less severe.
5) Intimidation: when you have a firearm out, people pay attention to you. When you have a suppressor stuck on the end, people know you really mean business. A suppressor has value here, just like a heavy 12g pump shotgun has more intimidation value than a plastic 9mm. This can be an advantage if you don't particularly want to have to kill someone (which is usually the situation cops are in).
6) They're really, really cool.