In game design, playing and reviewing a lot of emphasis is put on how fun a game is. This is probably not a bad thing, while the medium could surely grow and do new things while looking at other motivations I'm happy getting fun out of my games and there's still a lot of untapped potential. It may be too general a term, I think that I get a very different sort of fun out of Go than I do about of Ca$h and Gun$.
I think that every gaming professional hates fun. Wait, that came out wrong, let me rephrase it. I think that everyone who works with games has trouble with now nebulous the concept of fun is. We know when we've had fun, sometimes we know when we're having fun (though if we're having enough we tend not to think about it until we stop) but it's pretty rare to be able to identify why. I imagine this is a real headache for reviewers who know whether they enjoyed something but need to express why they reacted the way they did to an audience in order to write a decent review. It's possible to talk about components and theme and mechanics and all sorts of things, but sometimes the whole is more or less than the sum of its parts. Grasping why can be pretty tricky.
From a design point of view I struggle with marrying the concept of fun to objective truths. For instance, on a depth vs. complexity level I should remove the monkey from 404: Law Not Found. It is one counter that requires its own set of rules, in a lot of games it either never escapes its cage or is killed immediately and has no impact on the game. It only appears on a small subset of the objectives and there are other objectives that could easily replace them. Nothing about it contributes sufficiently to the depth of the game to justify spending half a page of rules on describing its behaviour.
Except that it's fun. The category for the posts about the game is still "Monkeygame" after some playtest groups that were really enamoured with the monkey wanted to name the game after that. It appears on the front cover because of how it's affected some player's experiences of the game. It's definitely adding something that goes beyond what I can express if I talk about the game as an abstract. Sometimes I really feel for particle physicists, finding something by looking at the effects that it has, rather than being able to directly observe it is hair tearingly frustrating. I can't express why in simple terms, but this game needs a monkey.
I now find myself trying to look at this from a player's point of view. Which games do I own that contain an element that from a design point of view might be considered an unecassary bolt on, but from a player's point of view adds to the fun. It's always hard to think about things that you like in negative terms, but it's an interesting exercise to try.
I wonder if capacity of a pawn to move two spaces on their first turn in Chess would qualify. The rule was added to get to the fun part of the game more quickly, but it adds a surprising amount of complexity. The double move rule necessitates the inclusion of the en passant rule, which is often a stumbling block for novices. Then again, chess has a very low mechanical complexity (not to be confused with the depth of strategy it offers) so perhaps this shouldn't count.
I've always found the inclusion of the pied piper title in Prophecy to be an odd choice. If a player kills both of the rats in the game they are named the pied piper and receive a tiny amount of money every time they enter the city or village. The rats are so weak that anyone who encounters them will almost certainly kill them and the benefit isn't big enough for it to be worth expending significant resources to ensure that you encounter both so in the vast majority of games the title is never awarded. Then again, this isn't a rules addition; there are plenty of small nods to things in card games, such as IMAGE IN THE MIRROR and NI EGAMI RORRIM EHT in Betrayal at House on the Hill.
There's a definite example in Twilight Imperium, someone felt it worth spending a column of rules to express how a single fighter can attempt to fly past a war sun's defences and blow it up singlehandeledly. This is very rarely a tactically viable option, more often than not it's statistically favourable to simply engage the war sun in combat directly, but the rule is there because someone thought it would be fun, both in execution and for the star wars reference.
It's been a while since I played any large scale wargames, but I remember that quirks and oddities that had been kept in for one reason or another were much more common during these games. I always found it a delight to field something unusual and create situations that me and my opponent had never seen before, I had a very unusual game at the worlds De Bellis Multitudinis tournament with the player seeded fourth, we'd both fielded some pretty unusual units with special rules (El S, Bow X, Ps X and WW O were the main ones for people who know the game) and the game still sticks out a decade later.
Often it's good to simplify and decisions should always be evaluated in terms of how they impact on the game's complexity - but the experience that the players have must always come first.