Oscars are somewhat infamous for getting sold as tiny little youngsters to unsuspecting hobbyists who don't realize these fish can grow longer than a foot. These fish can be moderately aggressive, though not unduly so for a large cichlid. When selecting tank mates, consider both oscars' size and demeanor.
Oscars can live comfortably in groups of their own species. However, in order to keep a group of oscars in the same aquarium, you need a huge tank of at least 350 gallons. Oscars do not need a group of their own to feel safe, however. A single fish or a male-female pair can successfully share a smaller aquarium.
Large Schooling Fish
Oscars can share a tank comfortably with large schooling fish. For example, silver dollar tetras (Metynnis spp.) come from the same general area and will not trouble oscars. However, smaller schooling fish will often wind up as bite-sized snacks for oscars. Believe it or not, a few schooling fish do get large enough to actually threaten oscars, including the pacu (Myleus spp.). The main consideration with midwater schooling fish and oscars is the respective sizes of the fish, since most of these fish have very gentle demeanors.
Other Large Cichlids
Oscars can share a tank with other large cichlids. However, you have to observe some important caveats. Stick to South American cichlids. Central American and African cichlids tend to fight with cichlids from other areas. Additionally, some cichlids can be belligerent enough to harm oscars. Cichlids from the genera Heros or Geophagus come from the same general area and have a peaceful enough temperament to share a tank without incident. Keep in mind that cichlids tend to have unusually distinct personalities for fish, and some individuals may be unusually aggressive for their species.
Oscars can easily share a tank with large, peaceful catfish. For example, larger plecos and doradids rarely cause problems in oscar tanks. However, a few fish in this category can act unusually aggressive. For example, while most plecos are quite gentle and rarely cause problems in aquariums, certain large Panaque plecos can be very ill-tempered and have sharp enough fins to injure other fish. While oscars are not push-overs, a large, mean catfish can dish out a surprising amount of hurt.