The two most common aquarium filter types are power filters and canister filters, so these are the filters I will cover in this article. Power filters are usually used on smaller fish tanks and canister filters are usually found on larger fish tanks. However this is just a generalization and either of them could be used on any size aquarium.
Power filters are also known as Hang-on-Back filters, because they hang on the back of the aquarium. The good thing about power filters is that they make maintenance very easy. When you need to clean the filter, you just pop the lid off and remove the filter pad. You can even leave the filter running when you do this. There are two possible issues with power filters. The first issue is that they stick off the back of the fish tank, so sometimes they make you keep the fish tank further from the wall then you might like. The other issue is that if your water level gets low in the fish tank, the filter can cause a lot of splashing, which will cause further evaporation and can be very noisy.
Canister filters take water from your aquarium through a tube that runs to a canister that rests under the aquarium. This canister is pressurized and the water is forced through the filter media and out another tube. That tube runs back to your fish tank. Canister filters don't have the evaporation problem of the power filters. They also take up less room behind the tank so your fish tank can be closer to the wall. The downside to canister filters is that because the canister is pressurized, you have to turn it off to do any kind of maintenance.