Fun little animated game with a physics engine that requires you to design a bridge with a limited budget in various scenarios. You get points for the amount of money you have left after completing a successful bridge.
NOVA Build a Bridge
Classic game from PBS.com that has you pick the right bridge design for certain scenario. This is a very basic game and good for younger ages.
A Bridge Design Game
Free and Open Source bridge design game. You have to make a free account at codeproject in order to download the game.
West Point Bridge Designer
Perhaps the most famous bridge building game, it certainly is a good one. Developed by engineers from the United States Military Academy, this is a free program for anyone to use and enjoy. They have a annual contest with scholarships for prizes.
FWG Bridge 2
Free online game for designing bridges. Has multiple levels.