The Adventurer
Loves to experience and nothing more. Loves the thrill of exploring a new world with new characters and eagerly awaits the next dungeon/town/level/region. Will play and buy games to explore them and quickly gets bored if nothing new is presented.
Quickly becomes bored of a game if they've seen everything even if they are not maxed level or geared out or if there's pvp.

The Story-liner
This gamer just want's the be immersed in an enthralling story-line with interesting characters that are facing tough decisions. This type of gamer likes to find answers.. and fast and absolutely loves 20 minute cutscenes and FMV's. Once the end credits are rolling the game is beaten and the disk is already being taken out... unless there is a secret ending after the credits. They care not for trophies, bragging rights or unlocks.

The Romance Gamer
Loves playing romance games like visual novels or dating sims. Can also apply to those who don't play such games. Gamers who like having some romance in the games they play as much as possible also fit into this category. Romance especially between the main characters of the game is what these gamers like.
I don't quickly become bored though. I also hate PVP.