Like all Mainstream Pokemon Games, Pokemon FireRed has compatibility with other games as well. Of course, since it was released with Pokemon LeafGreen and both are simply two versions of the same game, Pokemon FireRed can easily connect with it. By connecting Wirelessly in the Union Room, you can Trade, battle and crush berries with other players in Pokemon LeafGreen.
Since Pokemon FireRed was also released in the 3rd Generation of Pokemon, it can connect with other games that were released in the same. Unfortunately, since Pokemon Ruby & Pokemon Sapphire were actually released before Pokemon FireRed, they cannot connect with each other. Pokemon FireRed, however, can connect with the Hoenn Region Based Game, Pokemon Emerald. In order to connect Wirelessly in the Union Room with those playing Pokemon Emerald, you must first retrieve the Ruby and Sapphire during the Post Game so Celio can complete his machine.
Pokemon FireRed can even connect with a few Mainstream Pokemon Games that were released in the 4th Generation of Pokemon. When playing Pokemon Diamond, Pokemon Pearl, or Pokemon Platinum, you can insert Pokemon FireRed into the GBA slot of the Nintendo DS. When done, certain Pokemon Species will appear in given location in the 4th Generation Games after receive the National Pokedex. Players can even transfer Pokemon from Pokemon FireRed to one of these 4th Generation games by using this method (but not the other way around)!