You want theory? I gots theory. Three posts.
Let's start with a glossary of “Kinds of fun”. It's not complete by any stretch, but here we go:
AGON is the thrill of winning against another person at the table. This is not quite the same as beating a challenge, or about winning against difficult odds; it’s about beating the other people at the table. It’s not the most common joy of RPGs - in fact, a lot of gamers want to avoid it, since problem agon is really, really bad stuff. But it does sneak in. When the GM takes on the role of adversary, playing not just to embody the challenge fairly, but in an attempt to whup the players, that’s agon. When a couple of players engage in creative one-upmanship, trying to spout the coolest thing (in theatre terms, trying to upstage each other rather than collaborate), that’s agon again. Agon can be good, but only if it’s acknowledged and used, rather than festering quietly.
ALEA is the gambler’s thrill - the fun of taking a big risk, the tension that comes with it, win or lose. Games with dice rolls, and especially ones where big stakes are riding on that one throw of the dice, are good at giving alea.
CATHARSIS is a feeling of release that follows an intense or overwhelming experience. Not necessarily a tragic or traumatic experience, but usually an emotional one. Catharsis is served best by very particular kinds of phrasing in play - notably, talking in the first person regarding your character is often deeply helpful.
CLOSURE is the feeling that there is nothing more that need be done, and that the thing is finished. Closure requires resolution to whatever the matter at hand may be. This goal isn’t especially tied to any of the modes, but does require that either the GM make the in-character goals and end points clear, or that they actively listen to the players (in a way that often has some features like slow-moving collaboration).
EXPRESSION is the simple desire to be creative at the table; expressive players often spend plenty of time on description, might draw the characters, might write seriousbackgrounds (though big backgrounds also mark Kenosis and Kairosis)
FIERO is the feeling of TRIUMPH, of winning, of defeating a challenge, or overcoming adversity. People looking for that feeling are on the lookout for adversity – and they tend to want adversity where they can be partisan for their characters and the GM is actually playing against them a bit. If it’s not a real challenge, with real dangers, then there’s no payoff for a fiero-chaser. If you’ve ever died again, and again, in a computer game, and then finally manage to succeed, and felt a rush where you could stand on your chair and scream? That’s fiero.
HUMOUR… Games can be played for laughs, and often are. A player that really pushes for humour will often end up pushing for collaboration, even to the point of attempting to dictate the actions of other player characters, because some of the humor that comes to mind most easily can step outside the specific ideas of “who is in charge of what" often setups lay down.
KAIROSIS is the feeling that of fulfillment that comes when an arc of fictional development completes – a character is tested and changes, a situation grows more complex, and is then resolved, and so on. Actively seeking kairosis often means authoring, though it may only be authoring certain details relevant to you (revealing yourself from stunt-level disguise in Spirit Of The Century, picking out character developments from Fallout in Dogs in the Vineyard). If you find yourself saying "that was a good ending to that bit", you're probably experiencing Kairosis.
KENOSIS is the feeling of being deeply engaged in their character or in the fiction as a whole; it’s one version of “immersion”. Players looking for this (especially really serious kinds) often aim for a lot of characterisation. They also often (but not always) want to avoid types of collaboration that will pull them “out of the groove”. Serious kenosis is one of many “flow states” that goes on in tabletop gaming.
KINESIS is tactile fun. Miniatures, maps, game book illustration, tokens, and dice are all visual and tactile things that are enjoyable about RPGs. I haven’t yet met anyone that considers these things their number one priority, but it ranks in the top five things for quite a few.
LUDUS is for people who take their rules seriously. The tinkerers and the optimal builders are chasing this kind of fun. To someone looking for ludus fun, the rules are the game, a toy that the group is here to play with. Wherever the mechanics of the game are, whatever modes they attach to, that’s where ludus-seekers go. In order to support ludus, there needs to be enough complexity in the rules to allow someone to actually spend time exploring and playing with them as something interesting in their own right. D&D and Exalted both tend to satisfy ludus-oriented players.
NACHES is the enjoyment of seeing someone that you have taught, or are responsible for, go on to do well with that knowledge. If there’s a player at your table who is always happy to teach the others about how things work, chances are they like their naches. Many GMs, unsurprisingly, get a lot of good naches and enjoy it. Some players can get this same kind of enjoyment from seeing a student or smaller ally of their character do well.
PAIDIA fun is free-wheeling player fun, where rules are a convenience. Players looking to get some Paidial fun would prefer winging the rules-calls, going for whatever feels right at the moment. If there are involved adversity-resolving rules, Paidial players avoid adversity. Novelty and wonder are often, but not always, associated with this goal. Goofy characters are sometimes signals that someone wants this kind of fun.
SCHADENFREUDE is delight in the suffering of another - the thrill of seeing the villain get what they deserve is a pretty common expression. A game session can only provide this really well if it has characters that players “love to hate” and whom they inflict real damage (not necessarily physical) on without serious guilt.
SOCIABILITY is pretty central. For most gamers, the game and the acts that make up “playing the game” are a way of being social (for others, the event is also – or only – an excuse for being social outside of play). People looking to get especially significant gameplay-as-socialisation often try to match their other goals with the rest of the group, but do want to chat in general –if they aren’t engaging in characterisation, they will often enjoy general table talk.
VENTING is, simply, the desire to work out player frustrations or other emotions, using the game as a means. After a rough day working, smacking the hell out of some monsters can be pretty enjoyable.