Lord of the Ringsis more or less the foundation of modern D&D. The latter rose from the former, although the two are now so estranged that to reunite them would be an act of savage madness. Imagine a gaggle of modern hack-n-slash roleplayers who had somehow never been exposed to the original Tolkien mythos, and then imagine taking those players and trying to introduce them to Tolkien via a D&D campaign.
DM of the Rings provides examples of the following tropes:
Aggressive Negotiations: The unnamed DM becomes rather upset at the heroes for killing Saruman, Wormtongue, and the Mouth of Sauron in parley.
Aragorn: Yeah, let's speed this up. (kills the Mouth of Sauron) DM: What? You attack him? During parlay? What is wrong with you guys? This is the third time you've killed someone during negotiations! Legolas: And yet they keep falling for it! It's hilarious. DM: You're supposed to be a king! Can't you at least pretend to be one for a few seconds? Aragorn: If I hadn't shot him, Legolas would have. Legolas: He's right, too. I was just about to announce my attack.
All There in the Manual: The DM has most of the important story points in notes he wants the players to read, but of course they refuse.
Anything That Moves: Sometimes, Aragorn's tendency to mistake elves for women is taken as this.
Théoden: Aragorn, we are in no position to turn away friends, no matter how disturbingly attractive you find them.
When they first meet the riders of Rohan, Gimli rolls a 1 on diplomacy and addresses them with "tell me your name, horse f—" 'GIMLI!'. What makes it even funnier is that Gimli's player said that on his own accord. He was role-playing his own critical failure.
Then there's the time Aragorn rolls a 1 on falling off a Warg and therefore he can't fall off, which means he rides it over the cliff instead.
Also when Legolas tries to shoot Saruman. Subverted in that the DM ends up raving about how he killed Saruman before realizing Legolas scored a 1, so he changed it into killing Gríma instead.
Cutscene: This is basically how the DM wanted to run the game, and actually did it in a couple scenes, like when Gandalf freed Théoden.
Cutting the Knot: The players come up with increasingly ludicrous (and hilarious) ways to do this to the entrance of the Mines of Moria rather than come up with the password (which the DM ends up screaming at them in frustration).
Death of a Thousand Cuts: Not shown, but it's implied that this is how they get rid of the Mumak, as everyone keeps stabbing its toes instead of going with Legolas' idea of climbing up the creature and stab it in the eyes.
Faux To Guide: A lot of the blurbs present bad roleplaying as the proper thing to do.
Remember, nothing will spice up your campaign quicker than long descriptions of NPCs doing spectacular stuff while the players sit around and watch. Players tend to stay on the rails better when you place obvious landmines on either side of the tracks.
Glad I Thought of It: Aragorn overrules Gandalf's plan to attack the Black Gates and keep Sauron's eye fixed on the West by pulling rank as king, only to... declare they're going on the offensive to attack the Black Gates. (Until Sauron "cries like a little girl".)
Jerkass: Everyone is this in one way or another, but the DM takes the cake. Everyone else's tendencies can essentially be blamed on him anyway, as most of their own jerkass moments are provoked by his railroading.
Done on purpose when they first meet Legolass... Leggo of my ass... Legolas.
Aragorn: He should have been named Leggo of my ass, because you're going to be saying that a lot.
And then getting the names right, but referring to them wrong.
Aragorn: Hail to the king, baby! Aragorn, son of Andúril, is back! DM: Andúril is the name of your sword, dumbass.
Frodo would like to remind you that his name is not Dave.
Mythology Gag: The DM asks why Aragorn isn't using Andúril (the reforged sword of his ancestor). Aragorn asks when he got that and the DM realizes he forgot to give it to him at Rivendell leading to a hasty visit from Elrond at the Rohirrim camp. This is a reference to the differences between the books where Aragorn got Andúril at Rivendell and the movie where they had to have Elrond visit him at the camp.
DM:The walls crack open, and thousands of skulls are released! Legolas:Oh Crap. DM:They tumble down from above, forming a great avalanche of death. The horrid sight is— Aragorn: Skulls? Like, only skulls? DM:Yeah. Aragorn: But that makes no sense! [...] Gimli: I'll bet this was a robust culture. Imagine their funerals... "Oops, Granny's dead, let's lop off her head and chuck it into the big bin to be dropped on adventurers."[...] DM:The skulls continue to pour in, filling the room and threatening to crush your nitpicking, over-analyzing characters. Aragorn: No problem, I'll just roll my saving throw vs. ridiculous contrivances.
Off the Rails: Defied by the DM most of the time, save for when the players get the drop on him. Like when Legolas gets a critical/max damage and ends up OHKO-ing Gollum.
Perpetual Poverty: The party is really unlucky when it comes to looting. And really frustrated about it.
Legolas: How's the looting going? Gimli: I've searched all the bodies (read: a pile of scorched orcs), and we got just enough gold to buy an ale. (beat) Legolas: You mean one for each of— Gimli: To share.
One of the most obvious examples. The DM clearly has a big conversation planned between Gandalf and Wormtongue. After Wormtongue's first line, Gimli's player steps forward, interrupts Gandalf's response, and introduces the party. The DM repeats Wormtongue's line and continues with Gandalf's response as if that simply didn't happen.
Legolas: Oh no. It looks like we've entered a non-interactive cutscene. Aragon: Entered? We've been in one since Rivendell. Gimli: I don't suppose we can hit X to skip? (Gandalf keeps talking to Théoden) I guess not.
One amusing version comes at the scene where Éowyn asks to join the group. Aragorn is totally okay with it, but the GM keeps on acting like he followed the novel and said no. After a few attempts at straightening things out, he eventually just writes her off as a nut and leaves.
Reading Ahead In The Script: Turned into a pretzel in strip XXIX when the DM reads the "Gandalf Returns" script instead of Galadriel's. Upon realizing his mistake he tells the players to forget what they heard, but they weren't listening anyway.
Players Gone: Boromir (because he's dead and wants to stay that way; see I Die Free), Frodo (because Dave wanted to play a Star Wars campaign, with him DM'ing), Sam, Merry, and Pippin (who went with Dave).
The hobbits eventually return late in the game, but this time, they are NPCs.
Seinfeld Is Unfunny: invoked In regards to The Lord of the Rings influencing D&D, as Aragorn comments that the party has been fighting nothing but orcs (also, the blind pond squid being called Watcher):
Aragorn: Whoever wrote this story has no imagination at all!
Shaggy Dog Story: After everything the players have gone through, nothing they do in the end matters and the story is determined by Frodo (who at that point is an NPC) succeeding at a will save. Aragorn and Gimli are not amused, but Legolas thinks it's hardcore.
Shall I Repeat That?: Actually defied once. When none of the players were paying attention when Elrond was giving them the backstory at the Council of Elrond. When they're asked what to do with the One Ring, no-one even has a clue where the conversation went, so...
Elrond: As you wish. I shall repeat my tale. Gimli:NO! I mean... Heh.
Take Your Time: Three days after the armies left Minas Tirith for Mordor, the DM reminds Aragorn that he forgot to heal Éowyn and the hobbits that were wounded in the previous battle. So, instead of leaving them to their fate, he decides to go all the way back, heal them and come back, leaving the army waiting on the road for six in-game days without any consequences.
Wall of Blather: Whenever the DM engages in narrative. Much of it is obscured by the players' ranting, because they don't give a damn. Including in the very first page, which (tries to) establish the setting.