Well, Darkrai and Cressilia are sort of enemies, especially in Pokemon Mystery Dungeon Darkess, Time, and Sky. Kyogre and Grouden are famous for the fact that they had to sleep years to recover from their battle. This is not a couple, but I would say Giratina would be the enemy of Dialga and Palkia and vice versa, considering they banished it to stop it from destroying the universe. Tornados and Thunderus are the enemies of Landorus. They are terrified of Landorus because it banished them or something.
Source: My memory of the National Pokedex, the legends you hear in the games, and the movie Giratina and the Sky Warrior, where I learned a bit about Giratina.