From Bulbapedia, the community-driven Pokémon encyclopedia.
The Eon Ticket (Japanese: むげんのチケット Infinite Ticket) is an event key item in Pokémon Ruby, Sapphire, and Emerald. It cannot be obtained normally in-game; instead, it must be downloaded at a promotional event or using the Eon Ticket e-Card.
With the Eon Ticket in the Bag, players are able to travel to Southern Island via S.S. Tidal once the Elite Four have been defeated. This is where the version-opposite eon Pokémon can be battled and caught: Latias in Pokémon Ruby and Latios in Pokémon Sapphire. In Pokémon Emerald, the Pokémon not selected to roam after the Elite Four's defeat will be present. The eon Pokémon do not flee from battle.
Distribution methods varied worldwide. In North America, the Eon Ticket could be transferred to the games through Mystery Events using an e-Reader and the Eon Ticket e Card. In Europe, it was possible to get the Eon Ticket at promotional events, but it could also be downloaded through Mystery Events from special Nintendo cartridges via link cable.
A player that received his/her Eon Ticket from either the e Card or a promotional event is able to share a limited amount of Eon Tickets with other players by mixing records. However, Eon Tickets received by mixing records cannot be shared further. Mixing records is the only way to obtain the Eon Ticket in Emerald.
A physical copy of the ticket was available through Nintendo Power magazine, volume 173.