Aside from the high stats shared by most legendary Pokémon, many of them are only available once to the player in a given save file, and to obtain another legitimately, one must trade with another game. The gender of most legendary Pokémon is unknown (though there are seven notable exceptions in Latios, Latias, Heatran, Cresselia, Tornadus, Thundurus, and Landorus), and all but Manaphy are unable to breed in captivity, even with Ditto (and Manaphy only produces the unevolvable Phione when it breeds with Ditto).
No legendary Pokémon is known to evolve, though many are part of a legendary trio or legendary duo. Much like starter Pokémon appear at the beginning of each regional Pokédex and their generation's portion of the National Pokédex, legendary Pokémon typically appear at the very end of them. There is one exception: Victini. Victini's Unova Pokédex number is #000, coming before the region's starter Pokémon in the Pokédex.
They also tend to have control over some part or process of the world, such as Suicune and the purification of water.