The wrench in it's various forms has been used as a blunt weapon. A universal melee attack has been a downward swing using the heavy end of the wrench. The most popular wrench used in games to do this action is the pipe wrench aka the monkey wrench. This is most likely due to its great concentrated weight at the end. Most melee weapons do not have an alternate usage/function but in Half-Life: Opposing Force the wrench can be used in a charge attack using the alternate fire in the game.
The wrench as it's mainly used in the real world is used to tighten or loosen things. Although primarily a melee weapon in games, it has been used to repair in game items. The most notable example of this real world use is Team Fortress 2 in which the Engineer class uses his wrench to build and repair his buildings. The virtual world disconnect is that in order to do this, he merely smacks the object that needs repairing. A loose connection to this is the use of wrenches or semi-wrench items (like pliers) to repair vehicles in a games like Battlefield 2, Battlefield 1943 or Enemy Territory: Quake Wars. In these types of games, another generic motion such as twisting the pliers above the object also does the job of repairing. The wrench has mostly been associated with an engineer class in various games, although, it also served as a repair tool for other classes, including Battlefield 1943's infantry class.