Invertebrates like snails, shrimp and crayfish can add an interesting focal point to an aquarium. These pets aren't fish though and have their own needs and behaviors.
Invertebrates are the shelled animals that you can put in your aquarium. The freshwater tank has a much smaller selection than marine tanks do but an invert or two can add a lot of interest to a tank as well as some special considerations. The most commonly kept inverts in the freshwater aquarium are snails, shrimp and crayfish. Freshwater clams are sometimes also available but they are mollusk a special group of inverts that are filter feeders that can be hard to feed in the confines of the freshwater aquarium so these should only be attempted by experienced aquarist.
As far as inverts go snails are by far the most popular. There are small pest varieties that sometimes get introduced when live plants are added but there are also larger ornamental varieties. The biggest variety is called the apple snail; they have a smooth round shell and can get as big as a tennis ball. These are pretty hardy but like all inverts are extremely sensitive to copper in the water either from old pipes or certain medications. Snails also naturally eat plants especially many of the softer bunched varieties sold for the aquarium.
Another common variety is the ramshorn snail whose shell is shaped like the spiral horn of a ram. They can get up to about two and a half inches in diameter and come in brown, striped and albino varieties but tend to be a little less hardy than either the Apple snail or the third common type the mystery snail. The mystery snails have a more rounded shell like the apple snails but are smaller often no more that an inch and a half in diameter. They come in brown and golden color varieties.
Another invert option are the shrimp these come in small decorative varieties as well as larger prawns. Keeping either in a community tank is usually a tricky thing to do as fish tend to eat the smaller ones and the larger prawns naturally eat fish.
The third option is the crayfish. These come in the common brown variety as well as red, white and blue varieties. There are also multi-color varieties that come from Australia and Asia. All of them eat fish and tend to be on the hunt when the lights are turned out, the same time many of your fish settle to the bottom. These also shed their shell to grow and are at risk from the fish until the new shell hardens.
So to sum it all up snail are the easiest invert to keep by far but do have a tendency to escape so a tight fitting lid is required. If you keep the small decorative shrimp with anything other than some very small tetras be prepared for them to eventually wind up as feeder shrimp. The larger Prawns will eat smaller fish in the tank, it may take a while but eventually it will happen and the same goes for crayfish. Both of these also become vulnerable for a short period of time when they shed their shells giving your fish a chance to turn the tables. Any of these definitely don't mix with the larger fish like cichlids in particular who normally feed on them in the wild.