Examples of video games that require the player to be online and play with other people include "Team Fortress 2", "Counter-Strike" and "Monaco." The genre of MMOs also generally has this requirement.
As of April 2015, there are thousands of massive multiplayer online games and multiplayer online battle games that require the player to, at a minimum, be connected to their server and share physical space with other players, even if they are not strictly required to cooperate with or combat them. Other popular examples of this genre are "League of Legends", "Heroes of Newerth", "The Lord of the Rings Online" and "EVE Online". A very early example of this type of game that predates the Internet was the BBS door game. Some famous examples were "TradeWars 2002" and "Nethack."
There are also some games that require players to be online and engage with other players, but which are not considered MMOs because their game sessions involve smaller groups of people. Many of these are first-person shooters, such as "Team Fortress 2", "Counter-Strike: Global Offensive" and "Day of Defeat." One example that breaks this mold is "Monaco", a combination platformer and puzzle game that has players work cooperatively to pull off heists.