Anvilicious: Like most animated films today, the Power of Friendship is presented in full force. Unlike most animated films today, it manages to work in the movie's favor (e.g. Kuzco is a total jerk, but he becomes a better person as he spends more time with the much nicer Pacha, and their cooperation helps get the both of them out of certain issues).
Ass Pull: Yzma and Kronk getting to the lab before Pacha and Kuzco, especially after being hit with lightning and falling into a ravine. Like everything else this is lampshaded, complete with handy pull-down chart.
Kuzco: No way. No way! How'd you get here before us?!
Ymza: I— ...Eh, how did we, Kronk?
Kronk: Well, ya got me. By all accounts, it doesn't make sense.
Yzma's Villain Song ""Snuff Out The Light" was for Kingdom of the Sun but was recorded before the animation even began. They couldn't use it for the movie since its exposition is different from the final product's plot. The song was put on the movies soundtrack. though, saving it from being a lost track.
Ho Yay: Kuzco and Pacha. Come on, you saw it. They had Kuzco dress up as a woman and pretends to be newlyweds with Pacha, Pacha almost giving him CPR and claiming "it was not a kiss", the amount of awkwardness between the two (including after they hug!), and Kuzco's Tsundere dynamic with Pacha. Oh, and Kuzco constantly ordering Pacha to take him back to the palace has eventually been shortened to "take me back" over the course of how many times it's been said. What more proof do you need?
Though, this one in particular has become a Discredited Meme as Tumblr has gotten more and more politically correct (as Kuzco "does not and never has identified as female", he can't be called a "princess"), leading to quite a lot of “Stop Having Fun” Guys when the subject comes up.
The poison. The poison for Kuzco, the poison chosen especially to kill Kuzco, Kuzco's poison.
"Uh-HUH, uh-HUH, uh HUH!"
"Don't tell me, we're about to go over a huge waterfall." You do the rest.
"Yep." "Sharp rocks at the bottom?" "Most likely." "Beat Bring it on."
This screencap of Pacha◊ has seen a burst in popularity as a reaction image, usually as a gesture of approval or to when things go juuuust the way you wanted it to. It also has been edited to include other characters.
The PlayStation, Dreamcast, and PC game was just as humorous and satirical as the movie is, hanging lampshades on video game clichés long before The Simpsons Game did. However, there are changes to the plot, such as game Kuzco knowing Yzma is trying to kill him right from the start, while in the movie he did not learn that until after the diner scene. We should also note that Yzma's crocodiles are, shall we say, more competent guards than they were in the movie.
Seinfeld Is Unfunny: Aside from the whole "twisted, snarky fairytale with an all-star cast" concept being monopolized by the runaway success of Shrek (which made it to theaters months after The Emperor's New Groove did), this was also the first Disney film is years that was not a blockbuster musical romance with a "Be Yourself" message. Anyone who doesn't remember this era will probably have a hard time getting past the "David Spade as a llama" gimmick.
Sequelitis: The direct-to-DVD Kronk's New Groove was dire, save perhaps one or two individual moments. The follow-up TV series The Emperor's New School regained some lost ground but had a tendency to take jokes from the original movie and re-re-re-use them until they lay in tatters.
Trailer Joke Decay: Averted. The "huge waterfall" scene was already funny out of context, but is so hysterical in-context that it remains fresh.
Vindicated by History: The film was eventually a modest money-maker, and has garnered a new lease on life in the post-Shrek world as an example of how to do a timeless animated comedy right — many of the gags aged far better than the heavily modern pop-culture based humor of Shrek and its knock-offs, and the character of Yzma is now viewed as one of the best Disney villains.
Woolseyism: When Pacha first meets Llama!Kuzco and questions this, Kuzco answers "Yeah, who do you think you're talking to?" In the Norwegian dub, they apparently found it hard to fit the lip sync and instead had Kuzco mockingly mimic Pacha's question, which somehow made it even funnier.