Overall there are three different types of gamers out there; the creators, the explorers, and the acheivers. The creators are alot mostly represented in games like minecraft where you are allowed to wonder the world, settle down somewhere and begin to build a home settllement or city. Games like Sim city and Minecraft. The explorers mostly enjoy the games where they can explore an open world and their decisions make a difference in said world. Games the explorers enjoy tend to be alot like Fable or the mass effect series. The acheivers enjoy games where they receive a senes of accomplishment such as Mario or the multiplayer modes of the major first person shooters. 
Few players are really just one type of gamer, more often then not each gamer will lean in the direction between two of these themes. In order for a game to truly be a great game it needs to apeal to at least two of these gamer types. Then there are the games that apeal to all three, for a lack of better example take Minecraft.  Minecraft has an open world that let's the explorers explore the creators build, and a small acheivement  with an increadible ending apeals to our achievers.