Awesome Art: As per usual for Disney's eighties cartoons, some of the episodes look amazingly close to the original film's quality for TV budget, especially the early episodes produced by TMS or Disney's Australian unit.
Accidental Innuendo: In "No Rabbit's a Fortress", Tigger tells Pooh and Piglet that he will lead them past the booby traps, and follows it with, "Tiggers is experts on trappin' boobies, y'know!"
Awesome Music / Ear Worm: The theme song. It was so kicking that all agree that the theme song is one of the best things to come out of the franchise. It's likely a whole generation of kids who grew up watching One Saturday Morning, the Pooh videos or other reruns have the theme drilled into their heads.
The closing credits instrumental version of theme song, particularly the extended version with humming and just a bit of vocals at the end.
Many of the music cues and background songs.
The pirate song from the beginning of the episode "Rabbit Marks the Spot". It is one of the most awesome and fun pirate songs ever.
Big-Lipped Alligator Moment: Private-Ear Tigger's Disney Acid Sequence in "Eeyore's Tail Tale", which comes completely out of nowhere after Pooh hires him to look for his missing "Bee Tickler", and accomplishes nothing after it's done, with not one word being said about it, leaving audiences to wonder "What was that all about?"
Bizarro Episode: A fair few episodes step out of the usual laid back antics of the original film and books and take a far more surreal tone, most notably "The Piglet Who Would Be King", "Cleanliness is Next to Impossible" and "Sorry, Wrong Slusher.".
Nasty Jack, a literal horse, from "Paw and Order", to the point where he's playable in Mugen.
Kessie from "Find Her, Keep Her". Everyone remembers Kessie. This is probably why she was promoted to main character in The Book of Pooh.
Stan and Heff from "The Great Honey Pot Robbery" have quite a following, too, if DeviantArt is anything to go by.
"Funny Aneurysm" Moment: In "the Wishing Bear," the rest of the gang tries various ways to jog Pooh's memory when he forgets the rhyme needed to make a wish Christopher Robin's wishing star. The plot of the gang trying to help Pooh's memory was played much more seriously in Kingdom Hearts II when the Heartless tear pages of the Winnie-the-Pooh book out, which causes him to lose his entire memory.
For similar reasons as the above, the episode "Tigger Got Your Tongue?" had the characters thinking Pooh's honey, Tigger's voice, and Rabbit's vegetables were stolen by a "Nobody", with talk of whether "Nobodies" existed or not being frequent in the episode.
Pooh's cries to find the wishing star in "The Wishing Bear" become this when in Pooh's Grand Adventure, he similarly begs for the wishing star during his heart "Wherever You Are" - because he's "empty and [cold], and [his] heart's about to break".
The end of "Ground-Piglet Day" has Rabbit reveal that it's actually November 13th, which prompts Tigger to exclaim "November 13th!?" and gasp in horror, asking "Do you realize what this means?" He then goes on to say that it's "Porcupine Day", but after the November 13th of 2015 and the terrorist attacks on Paris, his intended over-the-top reaction to the date comes off as much more uncomfortable.
Genius Bonus: In "No Rabbit's a Fortress", Gopher mentions that he has U235 in his arsenal of explosives.
Harsher in Hindsight: Several episodes deal with the theme of growing up (especially "Grown, But Not Forgotten"), and the theme would receive the most focus in the Darker and EdgierPooh's Grand Adventure: The Search for Christopher Robin. That film in general makes many of the moments in this series between Pooh and Christopher Robin much more bittersweet, as in hindsight, you now know that those precious moments are on borrowed time before Christopher Robin grows up and can't come to the Hundred Acre Wood regularly anymore.
Two ditzy friends, one with a mostly red and another mostly yellow color palette, go on adventures that get on the nerves of their neighbor, a stuffy green-colored fellow with Super OCD. Did we just describe Pooh, Piglet, and Rabbit, or Spongebob, Patrick, and Squidward? It's even more hilarious since Tom Kenny, the voice of SpongeBob is the new voice of Rabbit as of the 2011 Winnie-the-Pooh film.
Ho Yay: In "Un-Valentine's Day", Tigger is first to play the romantic lead in the valentine Rabbit is directing, but when Rabbit tells him he's got to kiss Kanga, Tigger is disgusted and refuses. Rabbit pushes for it, and Tigger agrees to do the kiss...but then immediately leans over and kisses Rabbit instead. Also, in "No Rabbit's a Fortress", Tigger lamented about how he hadn't given Rabbit a "good bouncin'" in days, saying, "I feel an empty spot in my life."
Memetic Mutation: From "Tigger Got Your Tongue": 'Looks like polar bears eating marshmallows in the snowstorm'note Tigger mistook a white piece of sheet for a painting that Piglet was supposedly doing
Tough Act to Follow: While Pooh's follow-on series have their fans, The Book of Pooh and My Friends Tigger and Pooh are often considered paler shows compared to New Adventures due to it's impressive hand drawn animation, loyalty to the original film, clever emotional writing and wider scale target audience. The series set such a ground for Pooh works that some consider even the later feature length films inferior.