I'll Trade you!
There isn't a game in existence that utilises multiplayer and connectivity as successfully as the Pokémon series. Not only could players battle one another with a link cable (replaced by WiFi today), they could also trade one Pokémon for another – allowing the collection of new creatures that might not be obtainable in their version of the game. From a connectivity perspective, Pokémon was years ahead of its time.
With Pokémon Gold and Silver, we learnt where baby Pokémon came from – and it wasn't a stork. Apparently, all Pokémon are born from eggs. Since this startling revelation, players have been able to play cupid; matching together two Pokémon at the day care centre to see if they'll hit it off and have an egg. Some Pokémon, such as Pichu, are only obtainable through breeding, making it an incredibly important aspect of the game.