This will depend on what fish you have. There are several other creatures apart from fish that can be kept in an aquarium, including shrimp, terrapins, snails and frogs. However not all can be kept with fish. Some fish such as large cichlids will happily consume shrimp and small frogs. The size of the tank is also another factor to consider.
Their are a lot of things which can be put in an aquarium apart from fish, like plants, shrimp, terrapins, snails and frogs.
You can put a baby Turtle
Pleccy gives a GREAT answer! To add to his answer, some people also keep snakes in aquariums and pet spiders.