HOB: Cheap, easy, works. May have a little noise, especially the cheaper ones. They may or may not have problems priming after you lose power.
Canister: You can set up a water flow from one side of the tank to the other, easier to set up a more complex filtration system. Usually quieter, and better than HOB. But they're quite a bit more expensive, and if a seal blows...not good.
Wet/Dry (sump): You can use it to maintain a constant water level in the tank, you can put the heater there and not have it making the tank ugly. Absolutely the best for a saltwater setup, especially if you have something that eats copapods/amphibods. Also you can set it up to grow a ton of algae there, rather than mucking up your tank.
For a small tank the wet/dry is impractical. For a very large tank the HOB becomes impractical (you could run multiple ones, but you'd be better off with one good canister, or a sump). On my 55g fw I run a HOB Aquaclear, but before I was scared out of saltwater I did a 20 gallon sump.
EDIT: Oh, and I'd like to move to a canister system on the 55, since I've gone planted. The HOB is ok now, and is wonderful with just a fish setup, but I'd prefer a steady movement across the substrate.