Anticlimax Boss: First Archivist in The Second Sky. Despite being the main antagonist, he's fought halfway through in a short and not especially difficult level.
Breather Level: The Second Sky has a few. "Chronometric Ruins" is deliberately toned down, as it introduces a potentially confusing new mechanic, the temporal split token. "Caught in an Eddy" gives the player a chance to recover after some extremely hard levels, and allows them to explore the other surface. "The Scorching Path" is a breather level... for no particular reason.
Journey to Rooted Hold's music is all excellent, but particular stand-outs are "Brood" and "Uncovered".
"The Architect's Oath", the title screen theme of Journey to Rooted Hold, with a stunning harpsichord instrumental section.
The Second Sky has a number of pieces by Emmett Plant that play during story segments. Particularly awesome tunes include "Within These Swingin' Halls" (Halph's theme), "Waltz Recombinant" (First Archivist's theme), "An Architect's Dream of Geometry" (the Farrow Child's theme) and "A Sympathetic Bartendry" (Tendry's theme).
Occasionally, there's a full-on musical number. Usually, these crop up in Smitemaster's Selections, but there area few examples in the main games. They are all awesome, except "Use the Fuse" which royally succeeded at Stylistic Suck.
For example, the one at the end of Smitemastery 101, "Please Don't Name Your Sword", is a fun little tune about not naming your sword. It's actually a really catchy ditty, too!
Ear Worm: The title theme of Architect's Edition and King Dugan's Dungeon, "Whistler", which encapsulates the series' simultaneous silliness and epicness.
Goddamned Bats: Anything in the hands of a competent architect. Wraithwings typically get the most hatred, though, since they can fly, will run away from the player if alone (typically over pits) but in hordes, will swarm the player in a hard-to-predict fashion (since their movement is dependent upon the location of other wraithwings and the movement order of the whole horde).
Memetic Mutation: The fanbase itself has a lot of its own personal inside jokes that certainly behave like this in the community.
The Raygun, a parody of poorly made suggestions for features in DROD. It even got official recognition and Beethro got a Raygun in a bonus level of TSS; you can even get a bonus assets pack so you can use it in your holds!
Ketchup & Puppies. For some odd reason, one of the first custom holds was a little creation involving these two objects, with no puzzles in sight. Ever since, the combination of Ketchup & Puppies is not soon to be forgotten.
The H+S Effect/Curse/Syndrome/Phenomenon. Essentially, any time you post in the Hints and Solutions board on the Caravel Forums, only to figure out the room moments after posting. This can be very frustrating if you're someone from the future with the same problem and don't get the curse to hit you. Some people get this chronically; Hilarity Ensues then.
Scrappy Mechanic: Percentage damage in DROD RPG. In holds that contain hot tiles or Aumtlich (which remove 5% and 50% of your HP, respectively), you have to keep your HP as low as possible to limit the damage. This means leaving potions untaken and, when you need to regain HP, running round to take exactly as much as necessary. This is not a big problem in the main Tendry's Tale hold — it contains only one Aumtlich, directly after a huge Flunky Boss battle that will leave you very low on HP anyway, so it's more a one-off trap for the unwary than anything else. But some usermade holds contain far more of these elements.
Stealth Pun: The Living Tar (literally, tar that is alive) might be one on a part of the phrase "Beat the living tar out of him."
That One Achievement: With the advent of Challenges come TSS, of course a few of them would cause ire.
JtRH - Unnecessary Complications: In Level 2 4E, you have to clear the room and don't move Halph until the western door is open, don't break any crumbly walls, and don't kill any queens until all doors are open. These arbitrary things make the room incredibly difficult; in fact, most actually rely on a glitch that lets you kill a few select queens so they can get the challenge and be done with it.
TCB - Whodunnit?: The concept itself is simple; you kill 186th guide, and then activate a cutscene for it later in The Fork. The problem is, you can't just go ahead and axe her later, and then go to the fork. No, you have to kill her when you're going through her level—she disappears otherwise. So you're left going ahead and killing her when you finish the level. Except... There's several intermittent levels inbetween when you kill her and when you activate the cutscene for killing her. So unless you did this on your first playthrough, you will be playing both Uncturage levels. Again. Made worse because TCB is not just a "sit back and relax" hold—you need to put brain power into clearing each and every room, so this can very easily become a marathon. It's telling that in a sea of those few puzzles and other difficult achievements, including mastering the hold this achievement resides in, this is one of the least obtained achievements in the Steam version of DROD.
GateB - Charge First, Think Later: In Daskeros Tower 4N, you have to clear the room before you lower the blue doors (which drop when you clear the rest of the level). Problem is, this is meant to be theoretically impossible so as to enforce clearing the level before reaching the exit, which is just beyond this room. Of course, it isn't; with expert movement and manipulation, one can clear the room all the same, letting you skip doing the rest of Daskeros Tower, but if you're a newbie, the game's target audience, this will be a pain.
Consensus says that Levels 8 and 13 of King Dugan's Dungeon definitely fall into this state, and there are also particularly nasty rooms spread throughout the series.
In Journey to Rooted Hold, it's Level 22, an exhausting run through several large horde rooms. Most of these don't require normal completion (i.e. killing all monsters in the same visit) but just getting through them so you can reach a different entrance and set off bombs. Yet somehow, just getting through these rooms is harder than completing rooms on other levels!
Some user-made holds are infamously difficult. Gigantic Jewel Lost comes to mind.
The official level set Beethro's Teacher consists entirely of Those Six Levels.
The Second Sky brings several. Shattered Mine, Temporal Anomaly, Experiment of Ages, Rapid Fortification, and Mother of All Roaches all fall under this category, and not even some of the bonus levels are immune; TSS has become rather infamous among players for having a surplus of Brutal Bonus Levels, especiallyDarts.
That One Puzzle: Each game has one or more rooms that have acquired particular infamy. This list uses DROD's usual coordinate system, e.g. "1E" means the room once east of the level entrance.
King Dugan's Dungeon: Eighth Level, 7S3E. Just mention "three tar mothers" to any DROD veteran and they'll instantly know which room you mean.
Journey to Rooted Hold: Sixteenth Level, 2S2E. A grid of obstacles interlaced with rock golems — enemies that leave piles of rock when you kill them. It's extremely difficult to avoid these clogging up the grid.
The City Beneath: Abyssian Fortress, 2S. Tarstuff clearing on a small platform, giving Beethro very limited mobility.
The Second Sky has quite a few. Shattered Mine 1E, Eye of the Storm 1E, WBCEND/Caber Testing Area 3S1E, Lemming Beach 2S4E, and Rapid Fortification 3S2E have all stumped many players.