Many people are familiar with Bartle's Player Types: Achiever, Explorer, Socializer, and Killer. These canonical descriptions evolved out of social patterns that Bartle observed in early MUDS (multi-user dungeons AKA text precursors of MMOs like World of Warcraft). Many game designers (myself included) use this model to plan, design and tweak multiplayer games like MMOs.
A key value of Bartle's system is to raise awareness that different people enjoy different types of fun. It's also useful for de-bugging some of the more simple-minded thinking around gamification - particularly the limited appeal of Achiever-style point, badges and levels. Here's a great video of Bartle exploring the limits and over-application of player types, and offering some actionable ideas for applying player types in practice to gamified systems.
In practice, I've found that Bartle's Four doesn't generally work well for casual, social and serious games and gaming systems. So inspired by this model, I've developed a different twist - "Social Engagement Verbs" that captures the motivational patterns I'm seeing in modern social gaming and social media.
Compete (similar to Bartle's Achiever)
competition drives social gameplay AND self-improvement (competing with yourself to improve your own metrics). People who enjoy competition assume everyone likes competition, but that's just one among many motivators - and often not the best, especially if you're serving a female audience.
Collaborate (similar to Bartle's Socializer)
collaboration and collective action are a purposeful, non-zero-sum way of socializing. From Facebook "likes" to Kickstarter projects, collaboration is driving many of today's most innovative and influential social systems. People who enjoy collaboration like to "win together" with others, and be part of something larger than themselves.
Explore (identical to Bartle's Explorer)
Exploring content, people, tools, and worlds can be a rich and rewarding activity. People who enjoy exploring are motivated by information, access and knowledge; stand-alone points won't mean anything to them.
Express (a replacement for Bartle's Killer)
self-expression is a key driver for modern social gaming and social media - and a major motivator for engagement and purchases/monetization. People who enjoy self-expression are motivated by gaining a richer palette and greater abilities to showcase their creativity and express who they are.
I've tested and evolved this model with dozens of clients and students. Here's one of example of how to "blow out" the model and identify the key social engagement verbs in your product, app or service.
As Bartle says, no model is the ultimate solution. Think of this as a useful starting point for thinking strategically about what motivates your players - and for designing experiences that will delight and engage them by targeting these motivations. Don't be afraid to tweak this model to make it apply more specifically to your audience and application - I do it the time.