In Omega Ruby and Alpha Sapphire you have a chance of getting one starter Pokemon from previous regions: Johto, Sinnoh, and Unova. After you beat the Elite Four, you will have to go to Route 101 and find Prof. Birch being chased by a Pokemon and/or his wife. At this point just like the start of your journey you can get a starter. This can be repeated several times, based on how many times you've beaten the Elite Four, and you will in turn be able to obtain different starters.

Unlockable	How to unlock
Johto starters (Chikorita, Cyndaquil, Totodile)	Defeat the Elite Four once.
Sinnoh starters (Turtwig, Chimchar, Piplup)	Defeat the Elite Four three times.
Unova starters (Snivy, Tepig, Oshawott)	Defeat the Elite Four twice.