Online multiplayer games are any games that require an online connection and feature multiplayer PvP, PvE or co-op. Not all online games have social elements. Some just use the online element as DRM for premium game currencies, such as Gems and Diamonds.
Here you can find the most popular online games that people are using hacks, cheats, Bots and Mods for. Keep in mind that cheating in such online games is often against the games ToS and can get you banned from playing the game.