Answer 1

There is the Battle Frontier...

Answer 2

You should complete your pokedex to gain access to rare legendaries like Jirachi and others

Comments

You can't get access to Jirachi and others by just completing the Pokedex...

Answer 3

Like coolunown said, there's the Battle Frontier to battle in, and you can also EV train Pokemon to fight competetively and fight with other people near you that still play Emerald / Sapphire / Ruby / Fire Red / Leaf Green.
Or you could always save your game for stuff and import if you ever get DS 4th generation games.

Comments

Like meeeeeee(I have emerald & fire red/leaf green & a lost ruby & sapphire

Answer 4

If you complete your Hoenn Pokedex, you can get one of the Johto Starters from Professer Birch.

Comments

* The entire Hoenn Pokedex excluding Jirachi and Deoxys.

Answer 5

how about trying to catch Rayquaza, Groundon, and the three legendary Regis. :)