Completing the Pokédex warrants various rewards from one generation to another, based on completing the regional and national Pokédexes. This varies from no reward to getting useful items. In all games, you get congratulations and a diploma from the game director for capturing all available Pokémon.
In the first two generations, you get no additional rewards. The first game where you get an additional reward is Pokémon Emerald, in which you get a Johto starter from Professor Birch for completing the Hoenn Regional Dex. In Diamond, Pearl and Platinum, merely seeing all of the Pokémon in the Sinnoh Pokédex gives you access to the National Dex, the Fight Area and the Survival Area. Later, in Black 2, White 2, X and Y, you receive the Oval Charm for completing the regional Dex, which speeds up breeding, and the Shiny Charm for completing the National Pokédex, which increases the odds of encountering a Pokémon of a different color. Black 2 and White 2 also reward you with a ticket to the Nature Preserve for seeing all Unova Pokémon.