Nothing happens. In Diamond, Pearl, and Platinum, you'll get seals for each Unown from the boy in Solaceon Town and the Ruin Maniac will be done digging. In HGSS you'll finish the side quest.
When you catch all the letters, that digger south of Veilstone finishes his tunnel, allowing you access to a new area and the final two Unown which are "?" and "!".
If you catch A-Z you get access to a special room where you can catch Unknows ? and !. That's all really.
If you catch Unown A to Z, you unlock a super special room where you can get Unown ? and Unown !. Worst reward if you ask me. After you catch those two, nothing happens.