In the Silent Hill series, fog is used equally to create an atmospheric element, as well as because of hardware limitations. For example, players must walk through an open foggy area; due to limited visibility, the only way to detect monsters is via audio cues provided by a radio..
It also can be used to change the way a player navigates an area or even the way a game is played. In a number of games in the SOCOM series, distance fog is used as a way to stay hidden at a distance while using sniper rifles; an effect known as "shadow sniping". In the fog, all that can be seen via a sniper scope is a silhouette of other players. It also can be used as a way to navigate through the maps, out of the line of sight of unsuspecting players.
Sometimes Fog is used to make objects in the distance fade in more naturally when there are technical limitations, hiding the clipping which is actually happening behind the Fog. This is best shown in games like The Elder Scrolls III: Morrowind.