It's a logical question, as most people who become interested in having their own saltwater aquarium have seen videos and film of underwater ocean scenes with schools of beautiful tropical fish, or have been to public aquariums where a multitude of fish swim freely throughout the displays. They have also seen freshwater aquariums with dozens of fish in small aquariums. Freshwater, saltwater, what's the difference? You should be able to put a lot of fish in a saltwater aquarium, just like in the freshwater aquariums, right? Wrong!
Rule of Thumb
The short "Rule of Thumb" answer generally accepted in the marine aquarium hobby is: "One inch of fish (measured from the nose to the base of the tail) per 5 gallons of system saltwater." The normal response to this answer is: "Is that all? Why so few?"
The answer to the question is a bit more complicated and takes longer, which is why the shorter, easier answer is normally given. The "allowable bio-load" (number of fish) for a saltwater aquarium depends on the size and efficiency of the biological filter, the efficiency of gas exchange, the water temperature, the fish species, size and mix, the type (again, the efficiency) of filtration used, as well as the amount of cover or hiding places for the fish when they feel threatened.
Potentially, you can house more fish in a marine aquarium than the Rule of Thumb allows. However, most saltwater aquariums, especially new ones with minimal filtration, lack a really efficient biological filtration system to process the fish waste. Saltwater critters are much more sensitive to tank toxins (ammonia, nitrite, nitrate, phosphate) than freshwater fish. Aquarium filtration systems which facilitate gas exchange to keep the dissolved oxygen levels at the top of the scale will support more fish than systems that keep the O2 levels below the optimum. The higher the water temperature and salinity, the less O2 the water will hold.
How Many Fish?
The types and species of fish, as well as the mix of fish and invertebrates in the aquarium, make a difference in the amount of fish that can successfully be kept. For example, a 6" Naso Tang will do quite well in a 55-gallon saltwater aquarium with a dozen Blue/Green Chromis (total 18" of fish, or 1.6 fish inches per 5-gallons) while the same dozen Chromis would not fare well with a 6" Volitans Lionfish, which would eat them! While this example exceeds the 1 inch per 5 gallons of water rule slightly, it is safer with smaller fish than with bigger fish. A 55-gallon aquarium would best house only about 12 inches of fish, so to be safe, limit it to holding three 4-inch fish or two 6-inch long fish.
A vast majority of reef fishes require a "house" or someplace to hide either to sleep or to retreat to when they feel threatened. The same is true in an aquarium. A stressed out fish will not live as long as a fish which can easily retreat to a safe place whenever they want. Rocks and coral can be stacked to create crevices and caves for the fish to hid in.
While efficient filtration systems can be designed and installed on a marine aquarium, most of the filtration systems available on the market (hang on/in tank filters with bio wheels or small filter pads) are easy and convenient to use and will work for the small biological loads that the "Rule of Thumb" allows. With bigger and more powerful filters (large canister filters or refugium filters) the number of inches of fish per gallon can exceed the Rule of Thumb.
The "One Inch per Five Gallons" Rule of Thumb may be a bit conservative for the experienced aquarist with a tank that has been running well for some time, but the novice would be wise to follow the rule. It's better to be safe than sorry.