Most often, connectivity occurs between a console and a handheld platform (e.g. GameCube and Game Boy Advance). This is not necessarily requiring two games interacting with each other since in the case of GCN/GBA connectivity, additional features are made available simply by connecting the GBA to the GameCube. When playing a console title like The Legend of Zelda: Wind Waker in which the GBA does not need a game cart inserted to enable the player to control Tingle on the GBA screen who can drop bombs in the area around Link on the TV.
So far, notable connectivity features are available between GameCube/Game Boy Advance, Sony PSP/PS3, PlayStation Vita/PS3, Nintendo DS/Wii, Nintendo 3DS/Wii and Nintendo 3DS/Wii U.