Depending on the type of tank you have, that will determine whether you or not you need a protein skimmer. However, if you have a saltwater aquarium, you really should consider a protein skimmer. Protein skimmers don't really work on freshwater. They're mainly just used on saltwater due to the attraction of waste molecules to the surface of air bubbles. In fresh water, there's just not that molecular attraction to allow a protein skimmer to work.
The way a protein skimmer works is, the organic waste that's in the water is attracted. The molecules are called hydrophobic. So they're afraid of water. They want to be associated with air. So when you concentrate air inside a filter, the waste molecules are attracted to the surface of those air bubbles. When they're concentrated enough, the air naturally rises, because air rises in water, and the waste that's on the surface of those air bubbles gets removed. So a protein skimmer is actually skimming waste. It's not skimming protein, even though it's called a protein skimmer. It's removing organic waste from the water.
So a tank that has a high density of fish or one that's overfed or even just a regular reef aquarium would benefit from having this piece of filtration on the tank. It's very easy to use. It doesn't use resins or expensive filter pads. It's just air and water moving around in a cylinder and allowing that waste to be removed by this process.
So I believe every tank would benefit from having a skimmer. A side benefit is that it oxygenates the water to proportions that you really can't achieve without using some kind of pressure-driven air pump. Having highly oxygenated water will stabilize your pH. It'll also allow your bacteria to have the oxygen it needs to keep your ammonia and your nitrite levels low. So there's a lot of added benefits from having a skimmer.
The only downsides to have a protein skimmer is that it is another piece of equipment to maintain, it does require a good amount of space inside an otherwise crowded filter, and there is a tendency to strip out some of the minerals and trace elements and amino acids from the water column that you are going to have to add by either doing water changes or adding supplements to the aquarium. If you have a protein skimmer on 24/7, and you don't do water changes and you don't add a lot of supplements, you are going to strip out a lot of these nutrients. Even though the corals will be nice and healthy because there's not a lot of algae because all nutrients have been scavenged out by the protein skimmer, they're not going to grow as fast, because it's filtered out a lot of their minerals and a lot of their vitamins and a lot of their foods. So if you're using a protein skimmer, you definitely want to add some of the stuff that the skimmer is removing.