I've identified thirteen distinct types of fun, and grouped them into four categories.
This is analysis, and not advice, but it's still useful to know. I mention it here, for the sake of completeness.
I feel like I've created something, and watched it grow. People are hard-wired to like working on things they control. Gardening is a good real-life example of this constructive behaviour.
In Agricola, players start with an empty farm. They build rooms, fences, and fields. They add crops and animals to their little farm. It grows, and they have created it.
Sometimes, the system does its own thing, but the player builds and manages the system. I like this even more than just building. The thing I've built does something! It's fun to create, and fascinating to watch.
Dominion is a deck-building game. You start with a weak deck of ten cards, but you buy new cards to add to it. On your turn, playing your cards is fairly straightforward and procedural. It almost plays itself. The real skill comes in choosing which new cards to add to your deck. You come up with an idea, add the appropriate cards to your deck, and see if it works.
I like to plan something devious and unexpected, and surprise people. This overlaps with some types of social fun. It's a kind of constructive fun, with a social payoff.
In the hidden-role game Coup, everyone is dealt secret "character" cards. Players can lie about who they really are.
I like to be the Duke. I gather lots of coins, which is what the Duke does.
Then, someone is about to whack me. I'm backed into a corner, with my defenceless Duke, so I say "Um, I'm actually the Ambassador, and I'm going to use his power to change to another character now."
It's such a feeble and desperate ploy, after a whole game of Duking, that someone challenges me. "You're not the Ambassador!"
As it turns out, I was always the Ambassador. I reveal my card — the Ambassador — and the opponent is eliminated. The seemingly feeble "I'm now the Ambassador" was always going to be the key move of my ruse.
I want to win, and have a good time, but I also want to battle against the game itself. I want to do better than I did last time.
Sometimes games contain a "stupid kind of fun", which has no strategy or challenge involved. It's just excitement. Don't reject this kind of fun. It might not be useful in your game, but it's a real type of fun.
This is a subcategory of Watching the Machine Work. Sometimes, I want to see what happens, because I have absolutely no idea what's going to happen.
In the pirate crew game Libertalia, each player plays a pirate character card from their hand, face-down. Then, all the characters are turned up, and they interact. Fighting, stealing, and looting ensues, based on what characters the players played. There's interesting psychological strategy here, but just seeing what comes of the chaos is highly entertaining.
When things are more random, lucky things can happen. They may not be fair, or good for the game, but they're exciting nonetheless. Winning on a poker machine is like this.
The blank tiles in Scrabble are easily the best tiles in the game. When you're in a tight game, simply drawing a blank from the bag is exciting. Each turn, there's this "lottery" to see what tiles you pull out of the bag. If the tiles were balanced and fair, this excitement would go away.
New things are exciting. I want to see new parts of the game, because it's basically just more game. Many story-based and legacy (ongoing campaign) games do this.
In the farming game Agricola, at the start of each game, you're dealt a handful of Improvement and Occupation cards, from a deck of hundreds of cards. These add a huge amount of replayability to the game. However, I also just want to see the new cards.
This is where the game is at a crucial moment. I cover this in a later article.
(Most social interaction is self-explanatory.)
This is when a well-themed game helps the player feel more like they're part of a real scenario, with real characters.
In Battlestar Galactica, players pilot a spaceship through space, on a desperate mission to survive. They move around the ship, performing various tasks. The ship is under constant attack by marauding Cylon ships, and some of the players are secretly Cylons, trying to sabotage the ship from within. The game does an excellent job of capturing the feel of the 2000's TV show.
Some games have beautiful artwork, or physically appealing components.
Colt Express is a Wild West shootout, but the board is a multi-carriage, three-dimensional train.
The farming game Agricola contains delightful tiny wooden animals and crops.
Sagrada has the players construct a stained-glass window out of translucent dice.
My gangster game often veers into dark or ludicrous humour. Players are always amused by the "Gatecrash" card, depicting an obnoxious "party bro" with an air horn bursting in through the door. The game is about criminality, but there are plenty of wholesome locations thrown in. Why wouldn't a brutal criminal want to visit Ice Cream Van? People always smile, upon seeing Goths and Anger Management Class. Unless your game is deadly serious, throw some humour in there.
The best humour in games comes from interactions between the game and the players, or between the game elements. A dog going to a restaurant is funny, if players do it. A card called "Dog Goes to Restaurant" isn't so funny.