I don't want to play a certain person. Can I prevent them from challenging me?

If you do not want to play certain people, you can create a noplay list. This is a list of players that cannot challenge you to a match, accept your seek offer nor can you challenge them. 
The noplay list is ignored for games in tournaments (Tomato system) and for pool games. (1-minute, 3-minute, 5-minute, 15-minute, 45-minute and 960-pool)

Command Line Method:
To add BrianSP to your noplay list type on the command line under your console: +noplay BrianSP 
To remove BrianSP from your noplay list type: -noplay BrianSP

Shortcut for BlitzIn interface: To add or remove a person to your noplay list, highlight that player's handle name, right click, select Edit List from the right click menu, then choose Noplay or Remove from Noplay from the sub menu.

For more information about noplay and other lists read "help lists"