In Shadows of Mordor you can avenge the death of your friends by fighting the Uruks that have killed them. The Uruks themselves seem to be shared between the games.
In Forza 6 you are asked to beat the lap times of other players who have played the race before you.
Forza Horizon 2 encourages players to join Clubs where essentially the open membership groups have people who don't know one another but have been pushed into association at the game's prompting.
The Club membership is then used to push competition for ranking inside the Club rather than globally in the game.
Forza Horizon 3 uses an interesting mechanism of recruiting Drivatar's to a line up that grants you bonuses on races depending on the lifetime success of the players in your roster.
You get told how many festivals you are appearing in and how many times you've been hired and fired.