These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: Considering that the soundtrack is entirely taken from famous ballet/classical pieces, all the music in this show might qualify.
Also, it's produced by Kaoru Wada, well known for the music of anime such as Inuyasha. Doesn't that just scream awesome?
Particular candidates for Crowning Music of Awesome are the "Waltz of the Flowers", which plays during Ahiru's first transformation into Princess Tutu in the beginning of the series and her final dance at the end of the series, the "Swan Lake Waltz", which plays during Ahiru and Rue's duel at the end of the first season, and setting the Demon Raven's revival to Danse Macabre.
Not in the show itself, but the award-winning Hold Me Now AMV deserves mention for helping to spark interest in the show.
Big Lipped Alligator Moment: A subversion; Femio actually resists Kraehe's attempt to take his heart in hilariously preposterous fashion. The subversion is the fact that the Raven and Mytho actually use this incident as evidence that no one will ever fall in love with the poor girl.
Fan-Preferred Couple: Very few fans actually pair Ahiru with Mytho, instead preferring to pair her with Fakir.
Foe Yay: Ahiru and Rue's relationship as rivals, and Princess Tutu and Princess Kaehe's relationship as enemies, at least on Princess Tutu's side.
"Funny Aneurysm" Moment: Episode 7 has a funny conversation between Drosselmeyer and Duck as his attempts to get her to reconsider throwing away the pendant backfire. Upon rewatch it becomes much more chilling, as this is the first real glimpse of how much Duck will suffer later on, and the first indication of how much Drosselmeyer loves tragedies.
Genius Bonus: Rivals Ghost in the Shell for the sheer number of these. Naturally, these are all related to music, dance, and so on, but most people would have to see the translator's notes to get half of these. Big example of Shown Their Work.
Ho Yay Shipping: You will get an "abusive boyfriend" vibe from Fakir toward Mytho; and depending on who you ask, there's also subtext between Ahiru and Rue, as well as Autor and Fakir.
An in-universe example occurs in episode 17, where a raven blood-addled Mytho temporarily regains control and performs the mime for love...in front of Femio. A good few hearts are broken by this "revelation".
Another in-universe example: When Fakir returns to school after being suspended, Mytho gives him a hug. Cue a roomful of girls screaming with delight. One even faints.
Fakir acts like a very possessive, abusive lover to Mytho. When you find out the reason is because Mytho has no self-preservation instinct in his heartless state, it makes more sense and turns the Ho Yay up a notch. Also, during the promotional video, Fakir and Mytho are seen dancing together, and Fakir embraces him from behind. And upon his suspension ending and Fakir returning to school, Evil!Mytho gives him a great big hug in front of the entire class, which they definitely take notice of.
Ahiru and Rue get some Les Yay as well, due to their status as rivals and, in their heroic forms, enemies Not to mention Rue picking Ahiru as her dance partner in episode 2. And telling each other "I love you" in the final episode. Not as romantic in context, but still!
To be more elaborate, the ever-so-epic Guitar Ninjas came into being when somebody posted this◊ image review of the series. No actual guitar-playing ninjas appear in the series, but Anonymous agrees that it is still a very apt metaphor.
Narm: In Akt 7, Ahiru has a nightmare. It involves Princess Tutu dancing towards Mytho on her tiptoes, and him screaming in fear. Uh...
In the first episode, Duck's declaration of, "I am Princess Tutu!" Note that at this point, we have no idea what that means.
Mytho's half-hearted screams in the first handful of episodes of the dub. Granted, he has no emotions, but it's still funnier than it is dramatic.
Periphery Demographic: At the end of the day, it is a kids' show, but its Gaiman-esque dark fantasy elements can attract viewers of all ages, including older men.
The Scrappy: Pique and Lilie can certainly wear on most viewers' patience, especially Lilie and her cutesy/sadistic attitudes.
They Wasted a Perfectly Good Plot: How interesting would it have been if Rue/Kraehe was REALLY the raven from the legend, as it was implied in the first half of the show before the actual raven appeared? The romantic angle would've been a neat twist.
Also the Book Men, we get so little information about them. Did any other people with the story power manifest? Have they been called into action before? How were they founded? Have they had to stop any other stories from coming to life?