Written in 2019
Modern 3D games have plenty of options of how to display what's going on on the screen. More action oriented game tend to use the third person perspective for a better overview and easier navigation, RPGs where you should enjoy traversing the world or games that are focused on delivering intense immersion often rely on the first person view.
Especially in games with individually created characters, players often would like to see their "creations" - so in some games, there is a "over the shoulder" perspective.
Especially Bethesda games like Skyrim or Fallout 4 utilize this perspective. Both games can be played in a first persion view as well as an over the shoulder perspective. Games that display their characters in an over the shoulder view usually offer a close view to the back of the character with the feet not being shown.
In Skyrim, the camera zooms out a little when no the character has no weapons drawn and the camera can be rotated around the character, just like in a third preson game. So this perspective is made for people who do not like to play in first person mode all the time, but the gameplay and controls strongly recommend using such a mode.
The examples above are fairly modern games. But was there something like an over the shoulder view in the past? In fact, some RPGs used that perspective in battle screens. One example is Phantasy Star II, which was released as early as 1989. At the beginning of the battles, when strategies are set, characters are seen closely from the back. Only when they perform some action, they jump forward and do their stuff. This visual element was even kept in later games and rereleases.
Other games, such as The 7th Saga or Mystic Ark also used to a battle screen where the enemies are in the background and the characters show their back to the players. Although in the case of those two games, the whole character was displayed so the game's battle screen is more of a typical third person view. Yet, for the record, this should also be mentioned.