After much philosophy, I've identified 16 prime emotions, not counting the negatives separately. Note that I'm not done with this - I'm sure this isn't entirely right, but it's close, and someday I'll understand it all. Also note that I had to fudge the English language a bit, even to the point of outright reusing names, because English was not invented by philosophers.

(Note that the "future-minded" emotions like fear and excitement are actually reducible to these; they're just the partial-certainty forms: if you think there's a 50% chance that something upsetting will happen, you'll experience half the upset.)

Emotion NameTrigger
Intrinsic, self-based
Gladness, Self-PityOwn percieved fortune
Companionship, LonelinessSharing one's thoughts and interests with others / being unable to do so (footnote below)
Intrinsic, power-based
Epiphany, FrustrationUnderstanding gained/lost
Pride, HumblingSkill gained/lost
Intrinsic, activity-based
Empowerment, DisempowermentUsing power / Having no outlet for such (footnote below)
Engagement, BoredomApplying one's skills and effort / Not having a need for them (footnote below)
Intrinsic, existential
Novelty Fun, BoredomChange/progression, stagnation (footnote below)
Exhilaration, RestlessnessBeing involved in big things / being irrelevant (footnote below)
Intrinsic, analytic
Appreciation, DisdainExperiencing good/bad works of art
Amusement, DisamusementHumor, failed humor
Ideal-dependent, self-based
Self-Esteem, Self-HatredAssessment of one's alignment with one's ideals
Satisfaction, RegretAssessment of the result of one's actions
Ideal-dependent, interpersonal-based
Admiration, DisgustOther wills in accord/discord with own ideals (footnote below)
Validation, EmbarrassmentBeing seen by others whose opinion we care about as being the way we do/don't aspire to be (footnote below)
Ideal-dependent, other-based
Empathy, SympathyWanted prosperity of other / unwanted suffering of other
Schadenfreude, AngerWanted suffering of other / unwanted prosperity of other (footnote below)

Footnote on Empowerment/Disempowerment: This encompasses the pleasure of physical exercise, but also things like the powerful feeling of the weapons in Halo 1 and the way a lot of CCG cards seem to play off their "awesome factor". It's also part of the enjoyment of winning at games in general (the other part being pride), and even the enjoyment of customization.

Footnote on Engagement/Boredom: This can be understood as the "fun of trying", whereas Empowerment is "the fun of winning".

Footnote on Novelty Fun/Boredom: This "feeling of progress" notion is the reason why game players seem to universally enjoy mechanics like having levels be locked until they've beaten the previous level, even though from a logical perspective it seems like this is strictly worse for the player.

Footnote on Companionship/Loneliness: This also explains why playing games with other people is almost universally much more fun than single-player.

Footnote on Exhilaration/Restlessness: This shows itself in a lot of ways, including getting to the climax of a good game or story, being on a large team and/or playing with stakes in a competition, and I think the enjoyment of spectating a prestigious tournament or similar is also a form. It can also show itself in more meaningful ways, such as playing an important role in one's real-world cause (although most people have little to no experience with that, myself included).

Footnote on Admiration/Disgust: The concept of "ideals" is one that took me a long time to pin down. I think it's "what you'd will if you didn't have a personal stake in it". So by this token you can admire someone for being closer to your ideals than you, whereas back when I just called it "other wills in accord with self", I couldn't understand how that was possible.

Footnote on Validation/Embarrassment: A lot of things about human behavior and psychology are explained by this.

Footnote on Schadenfreude/Anger: Sometimes, when you're having a really hard time with something (programming triggers me like this all the time), self-pity would be the "natural" response, but you might feel something you'd rather label as "frustration" instead. I believe this is actually the feeling I'm labeling "anger", and it comes from implicitly personifying fortune as victimizing you. The reason for doing this is that it can be more comfortable due to the shifting of the blame off yourself and thereby elevating your self-opinion. It can even lead to some synthesized schadenfreude when you finally get it working (I experienced this a lot when I was younger). One should avoid this though; it's worse for your productivity in my experience, and also you're likely to end up taking your anger out with other people and making their day worse as well.

A few notes about things that aren't on the list and what they're composed of: