There are several rewards that can be earned by completing the Pokédexes in the game.
Note that certain Pokémon that will not count towards these prizes at all – Mew, Celebi, Jirachi, Shaymin, Darkrai, Arceus, Victini, Meloetta, Keldeo, Genesect, Diancie, Hoopa, and Volcanion. (Deoxys, contrary to tradition, is now required because of the Delta Episode.)
This is because these Pokémon have only been given out at Nintendo Events and have not been obtainable in other means (except, again, Deoxys). Thus, do not feel obligated to obtain these for the sole purpose of, say, the Shiny Charm.
The Oval Charm is an item which greatly increases the rate at which compatible Pokémon in the Pokémon Day Care spawn Eggs. To obtain it, see all of the Pokémon in the Hoenn Pokédex and then visit Professor Birch in Littleroot Town.
The Shiny Charm is an item that triples the rate of finding Shiny Pokémon - Pokémon with a different coloration, boosting it from 1/4096 to 3/4096, barring other augments to the rate. To obtain this item, visit Professor Birch after catching all Pokémon in the National Pokédex.
Hoenn Pokédex Diploma
The diploma for catching all Pokémon in the regional Pokédex can be found after beating the Elite Four. Head to the Cove Lily in Lilycove and speak with the Game Freak director to view the diploma. You can then view it at your leisure when you install it as the Regional Award item in your Secret Base!
National Pokédex Diploma
This is obtained much in the same way as the regional diploma, but you must now capture all Pokémon in the National Pokédex. Speak with the Game Director again to obtain this one. It also can be installed into your Base under the guise of a National Award item.