Socialization refers to the various ways that players use games to connect with one another on an interpersonal level. Related appeals include conversation (through game chat during play, or made possible through in-game messaging), cooperation (supporting and helping one another during play), and generosity (helpful behavior in a more one-way direction, like giving gifts or helping a low-level player advance more quickly).
You could, of course, argue that socialization is an appeal of any entertainment medium, from discussing favorite books with a friend to attending a movie in a crowd. Games, however, can be (and often are) specifically designed to encourage particular kinds of socialization over others.
Rock Band, for instance, is fun in groups not just because multiple people can play at the same time, but because it actively fosters a sense of cooperation: Players rely on one another and can help each other. If one player does poorly, the song could end for everyone, so other players must be mindful about when to save floundering teammates by triggering "Overdrive" mode.
Many team-based action games also rely on conversation between teammates not just to chat about how your day went (though players use games as a social gathering for just that purpose), but also to share tactical information and plan group actions against opponents.
Less formally explored, however, are more one-way generosity mechanics -- helping out players without necessarily receiving a reward for oneself. That may sound like it would be a contradiction in terms: Once you design a system that recognizes one player helping another, doesn't that necessarily imply a reward for the charitable player, making this more appropriately described as cooperation? I'd argue that this isn't always the case, but such a system may have yet to be designed in a truly satisfying way.
FarmVille, for instance, does allow for cooperation-free generosity by giving players the option to send one another gifts at no cost. One could ask for reciprocity (and players often do), but some players happily use this feature simply because they enjoy giving gifts to others.
Unfortunately, the system is designed better as a marketing tool than as an appeal because the result is often unwanted Facebook messages notifying players' friends that they have a "gift" waiting in a game they don't play. Some MMORPGs also offer formalized "mentor systems" (see Shadow Cities or Final Fantasy XI), suggesting that there is room to actually design for such appeals, though this is more typically arranged by players through less formalized means.
Recreation refers to processes of renewal and pastime, which typically means using a game to adjust one's psychological or psychological state. Related appeals include mood-management (toward relaxation, elation, amusement, or other emotions), distraction (actively avoiding thinking of painful or difficult stimuli), contemplation (pondering thought-provoking issues), and exertion (getting physically energized through play).
The broadest of these appeals is mood-management. I offer this as a single appeal, rather than offering each type of mood-management as its own appeal (relaxation, amusement, excitement, etc.), not only because that list would quickly get unreasonably long, but to make a distinction between appeals as play-behaviors and emotional states as their end result.
That said, it's worth making note that mood-management encompasses a great many more states than "having fun." flOw, a slow-moving, soothing game, was specifically designed to show how games might encourage relaxation rather than elation. Shadow of the Colossus and Final Fantasy VII have received praise for sometimes effectively encouraging sadness over happiness. Players choose different games based on context, depending on their company and their preferred mood.
Contemplation is a related appeal, perhaps even part of mood management. Passage, for instance, is a short game with subtle implications rather than an obvious goal for "fun." It's a game that is calculated to make you think, rather than to make you enjoy yourself. Distraction is another related appeal, and one that may not sound very worthwhile, given that it can be taken to refer to shutting out other responsibilities that need to be dealt with (as with compulsive gambling, for instance). Even so, distraction is at the heart of why games make such excellent therapeutic tools in hospitals, effectively acting as non-medicating pain-reducers.
One of the main reasons I think it's important to give recreation its own category is that it includes the main appeals that have skyrocketed many so-called "casual" games to success, from Facebook and mobile "social games" to motion-control games on the Wii and other systems. Regardless of whether critics or designers find their tactics to be nothing more than extortion, the success of skill-free games like FarmVille and Tiny Tower should suggest that these games are giving players something that they want.
Rather than lamenting that players are unfortunate dupes, it's worth considering that maybe players are getting precisely what they want from these games, at a price players are willing to pay. And while many traditional gamers lament that Wii "shovelware" games do little to scratch the surface of what motion control technologies could do, it has done little to slow sales of the system. Even the least thoughtfully-designed Wii game might offer some opportunity for pleasant physical exertion in the hands of someone eager to cut loose in the living room.
Subversion refers to behaviors that run counter to norms and expectations, as defined by society and game logic alike. Related appeals include provocation (actively antagonizing other players through "inappropriate" behavior), disruption (breaking game logic and exploiting glitches), and transgression ("playing evil", such as killing friendly NPCs).
I group these appeals because each involves breaking some kind of rule. Provocation involves breaking implicitly agreed-upon social norms about how people are expected to act in games and in polite interaction. Disruption involves breaking rules hard-coded into the game -- and, if you use those rules to your advantage in a multiplayer game, breaking the aforementioned social contract of "fair" play.
Transgression is generally considered the least offensive of these, as the rules broken are broader cultural norms, and generally permitted by fellow players and game rules. Nevertheless, I group this sort of transgression along with the other subversion appeals because the root of enjoyment behind this activity is, as more than one person said in the course of my research, "being a dick". The basic appeal of each of these activities revolves around doing something you know you're not supposed to be doing.
I give these attention as valid appeals, rather than dismissing them as griefing, glitching, and cheating, simply because so many players enjoy doing this sort of thing that it may be helpful to avoid thinking of it as a deviant behavior. (For a comprehensive account, see Mia Consalvo's book, Cheating.) How can designers account for this appeal?
The most obvious answer, of course, is that actually accounting for subversion neuters it entirely. How can you encourage rule-breaking and also leave the thrill of breaking the rules? That doesn't necessarily tell the whole story, however. Designing a path for "evil" play is one way to offer a transgression appeal: In Fallout 3, for instance, the player breaks no game-logic rules by sharing a friendly meal with cannibalistic murderers or by selling a small child into slavery, but still gets to enjoy bucking traditional narrative expectations and social norms.
Designers can even formalize provocation in a game where copping an attitude might be an expectation of the community: The aforementioned player-on-player brutality of Gears of War (with the option to punch an opponent's face for several seconds even after you've beaten them) might arguably be called a formalized approach to griefing. These offer ways to break the rules of normal social conduct without breaking the rules of the game.
Admittedly, it's trickier to suggest ways to encourage players to actually break the game rules without running the risk of actually destroying the game (or at least crashing multiplayer servers). Cheat codes and Easter eggs offer a sort of sanctioned subversion -- breaking game rules on a controllable scale.
Could we imagine a game that even more purposely encourages this sort of appeal -- say, a Matrix-style science-fiction game where glitching actually makes sense in the context of the game world, and interesting glitches get formalized as part of the game rules? I certainly wouldn't want to be the one in charge of making sure the game doesn't fall apart as players scramble to find ways to do just that, but it would be interesting to see some developer try something like it. For now, subversion may represent the most unexplored category of appeals to date.