The Adventure Time episode "Finn the Wizard" has one of these, which Jake lampshapes Jake-style by excitedly shouting "Full circle!"
Avatar: The Last Airbender ends the second season as it starts off with the first season: Katara looking overhead and carrying a comatose Aang in her arms. The first scenario is positive, finding the boy in the glacier for the first time to be revived, whilst the latter is generally negative suggesting a total opposite that Aang is dying.
The War began and ended with the arrival of Sozin's Comet: The first time heralded the genocide of the Air Nomads, and the second time heralded their final member defeating the Firelord and ending the war.
The episode "Zuko Alone" begins with Zuko riding on his ostrich-horse, angsting and alone, and ends with (you guessed it) Zuko riding on his ostrich-horse, angsting and alone.
Also, the Opening Narration at the beginning of every episode ends with a shot of Aang that pulls up into the sky to show the title; the very last image of the series mimics this with a shot of Aang and Katara kissing pulling up into the sky to show the words "The End".
Similarly, the beginning of the first season finale mimics the Opening Narration perfectly, except for the backdrop being arctic, strongly indicating that, yes, Aang is now ready to save the world.
There is also a bookend if you look at the story chronologically: Roku, the previous Avatar, was best friends with the Fire Lord in a time of peace. After 100 years of war, Aang is best friends with the new Fire Lord, heralding a return of peace.
This is actually much deeper than that. Roku and Sozin, the Firelord who instigated the war, were friends since childhood. Their friendship came to an end because of Sozin's desire to expand his empire, and it was due to this same friendship that Roku allowed Sozin to live. Had they not been friends, Sozin would have been killed and the war would have never started. Aang and Zuko started off as mortal enemies, but gradually learned to like each other, cumulating in their friendship helping to stop the war. Presumably they remain friends until the day they died. To further this, Zuko is the descendant of Sozin and Roku, which devels into Fridge Brilliance territory as it could symbolize the friendship between his two ancestors.
Another in-story example: Roku learned Airbending alongside Monk Gyatso and was his close friend. Guess who later turns out to be Aang's teacher and greatest friend? Aang also turns out to be Gyatso's last pupil.
The last two comments actually tie together into one big bookend. Aang asks Zuko in "The Blue Spirit" if they could have been friends if things were different They were in another life, if we count Aang as descended from Roku, and Zuko from Sozin. Roku tells Aang that some friendships last longer than one lifetime referring to Monk Gyatso, and it turns out to be true.
The first season has Book Ends—in the first episode, when Zuko learns that Aang has returned, he starts obsessing and Iroh advises him to get some sleep, saying "a man needs his rest." In the last episode, Iroh and an utterly-exhausted Zuko find themselves on a raft after the Seige of the North. Zuko says that he's tired, and Iroh tells him that "a man needs his rest." Also, a highlighted by Avatar Extras the first season starts at the south pole and ends at the north.
The first book also has book ends in the sense that they begin by leaving the South Pole, and end by arriving at the North Pole.
Furthermore, what was the first place they visited after leaving the South Pole? The Southern Air Temple. What was the last place they visited before arriving at the North Pole? The Northern Air Temple.
The first time we see someone bending (aside from the opening credits), Katara waterbends. The last time we see someone bending, Aang waterbends.
Bringing it all full circle, both Avatar and The Legend of Korra end with the Avatar sharing a heartfelt moment with their love interest. Avatar ends on Aang and Katara, while Korra ends on Korra and Asami.
"On Leather Wings", the first episode, begins with Man-Bat startling a pair of cops in an airship, before swooping down with his shadow cast over buildings as he flies past. The Justice League Unlimited episode "Epilogue", which was originally meant as a bookend for the entire DCAU, ends with a scene of the new Batman's shadow cast over buildings as he flies past, before taking off into the sky and startling a pair of cops in a Flying Car. On both occasions, one of the two cops gasps "Did you see that?", voiced by none other than the Goddamn Batman, making Conroy's voice the first and last thing heard in the DCAU. And the BGM is a synthesized version of the B:TAS theme.
When the show was Un-Cancelled, the last image of the DCAU is Superman, Wonder Woman, and Batman racing towards the screen, with a final zoom in on the Bat-symbol. It isn't a perfect Bookend, but this means that the DCAU began and ended with Batman.
The episode Joker's Favor" begins with Charlie unhappy with his mundane life and the perspective of eating meatloaf for dinner, and ends with him happily going home even when his wife Bonnie serves him meatloaf. There is also the scenes that show Joker menacing Charlie at the end of the first act, that has a mirror on the scene of the last act of Charlie menacing the Joker (see the image at Hourglass Plot).
Batman: Under the Red Hood starts with Jason Todd's last day as Robin and ends with his first day. Also the beginning and the climax of the movie involves Batman, Joker, Jason, a crowbar and a bomb.
Code Lyoko uses this trope in many episodes as part of the plot — since, in order to stop XANA, the heroes have to rewind time to before XANA tries to attack the world, often reliving the same things that at the start of the episode, although usually adding some twist with their foreknowledge.
In Cyberchase, a typical episode follows this format: in the beginning the protagonists are trying to find a solution to one of life's many problems, then Motherboard contacts and pulls them into cyberspace to help handle some Hacker-related problem using math, then they're sent back (with very litte time passing in the real world) and are able to easily solve the problem using the math lesson they happened to have just learned.
The Dinosaur opens with Dan giving a skyward scream, the episode ends with a dinosaur giving one (well skyward rawr).
The Danny Phantom episode "Reality Trip" starts off with Jack attacking Danny from his home with an Ecto weapon. The ending does the same, except Jack doesn't miss (played for comical abuse, nothing serious). If anything, it represents everything going back to Status Quo after Danny alters the world with a Reset Button so that the big change of his secret identity reveal is just that—secret identity, including erasing his parents' memory of that knowledge for no apparent reason.
"Bitter Reunions" has Danny meeting Vlad for the first time, triggering a longstanding arcbetween the two where Vlad madly pursues Danny as his son. This is ultimately concluded in "Kindred Spirits" when Vlad stages his final, desperate plan to obtain Danny. He fails miserably, resulting in a Villainous Breakdown. The Book End is that Danny calls Vlad a "crazed up fruit loop" in both episodes; the first to start the saga, the last to end it. After that, they become bitter, bitter enemies.
There was also a couple of Book Ends in the first and last episodes of the series. In the first episode, Danny was contemplating telling his parents about his powers but ultimately decided to keep it secret, then in the final episode, they learn the truth. There was also one with Danny and Sam's relationship. In the first episode, they begin the long spanning arc of them denying they were dating. In the final episode, they finally got together.
The first and last episodes of the first season of DuckTales both feature brief appearances by Donald Duck.
Before Futurama was Un-Canceled for the second time, the fourth movie "Into The Wild Green Yonder" had a poetic Book End involving the main characters entering a wormhole which took on the appearance of the pattern of lights seen at the beginning of each episode.
The first episode also began with a countdown from 10 (to mark the new year), this movie ends with nearly every character in the series counting down from 10.
Also, before it was Un-Canceled for the first time, the episode "The Devil's Hands are Idle Playthings" end with a crudely animated Fry and Leela walking away together, just like how the series began with a crudely animated starship flying. This was pointed out in the DVD commentaries.
Meanwhile begins with Fry, Leela and Bender making their last delivery in the show to Luna Park, which is where they also made their first delivery in The Series Has Landed.
Another House of Mouse short, called "How to be a Rock Star" actually begins with Goofy crying on a bench. The short ends with Goofy crying on the same bench again, except this time, he's now accompanied by the recording studio manager in which he accidentally bankrupted with his new album.
A music video for the song "Minnie Mouse in the House" actually begins and ends with Mickey Mouse, Donald Duck, Goofy, and Pluto passing by the Hercules section of the prop room, respectively.
Kappa Mikeyuses these, in the form of takes of scenes in Lily-Mu, usually with Mikey screwing something up horribly at the beginning and doing it right at the end.
The first episode of King of the Hill opens with a far shot of Arlen at sunset with the city's water tower in the background, panning down towards the Hill residence. The final episode ends with the camera panning up from the house into the sunset sky.
Both seasons of Legion Of Superheroes work like this. First, Superman returns to the Kents' kitchen and muses that just as promised by Bouncing Boy, he's back just in time for dinner: the same dinner they smelled cooking when they left for The Future.
In the second, Brainiac 5's Ho Yay fantasy of heroically sacrificing himself to save Superman and dying melodramatically in his arms gets twisted around a bit. Superman calls Brainy his hero again, but it's Superman that's dying in his arms.
In one old Looney Tunes cartoon, Porky Pig is in the Navy on a battleship. At the beginning of the cartoon, the CO is doing inspection after reveille, when a bugler sounds the mess call. The CO shouts, "Last one in the mess hall's a softie!" and everyone rushes to the mess hall; unfortunately, Porky trips, so he's the "softie". Later, in the main plot, Porky becomes a hero by capturing a pirate submarine, and is honeored at an award ceremony at the end... When the bugler makes the call again, and the CO makes the same joke. This time it looks like Porky is going to get their first, but he has to rush back to get his reward, and then rush back.
Moral Orel: Both the first episode aired and the finale are Christmas specials.
The intro to each show has Orel waving to God. In the final episode, his baby daughter does the same.
The My Little Pony episode Bright Lights begins with Knight Shade giving a concert near Paradise Estate. The episode ends the same way, except Baby Half Note, Baby Lofty and Baby Heart Throb get to be Knight Shade's backup singers/dancers.
My Little Pony: Friendship Is Magic had Book Ends for its first season - to an effect. The first two episodes were about the ponies gathering the Elements of Harmony to defeat a powerful villain (Nightmare Moon), and the last two that were produced for the season involved the ponies gathering the Elements of Harmony to defeat a powerful villain (Discord). Although the last two episodes were produced for the first season, they didn't get aired until Season 2.
You could take it one step further. The first thing that the ponies do after defeating Nightmare Moon was get tickets for the Grand Galloping Gala. The last thing they do before defeating Discord is attending said event.
Friendship Is Magic is full of these. Some episodes have book ends in themselves, but the overall story contains some good ones as well. All three seasons begin and end in Canterlot; as noted above, the first season essentially begins and ends with the Grand Galloping Gala; the second season begins and ends with the near-domination of Equestria by outside forces; the third season, which was just full of continuity nods, begins with the ascension of the Crystal Princess, and ends with Twilight's ascension to princess-hood.
The Pink Panther: "Prehistoric Pink" starts with Cavemen Pink Panther and Big Nose pushing off a giant stone. The cartoon ends with the duo pushing off the same giant stone, apparently after all their hard work of inventing the wheel to make moving the stone faster failed.
The first Popeye cartoon from 1933 opens with Popeye on a ship, singing his famous Image Song. The last theatrical Popeye cartoon, 1957's "Spooky Swabs", ends with Popeye once again on a ship and singing his theme song.
The Recess theme song ends with the kids coming inside after recess is over, and as Miss Finster is about the close the door, T.J. comes up from behind her and waves to the audience, and she slams the door right after that (where the doors are closed for a few seconds while the "Created by:" credits are up until the fadeout to the episode). Recess: Taking the Fifth Grade (the 2003 Grand Finale) ends with the exact same scene. This became somewhat of a Tear Jerker to fans who have watched the show since the very first episode, and now know that it's the end.
The Rugrats episode "Slumber Party" both technically begin and end with Tommy asking what a slumber party was and Angelica replying "If you hafta ask, you'll never know."
In Scooby-Doo! Mystery Incorporated, the main characters rejoice in the first episode and state they should celebrate. They do this again in the final episode, down to the exact same poses.
Shadow Raiders begins and ends with The Beast consuming a planet. Yes, its ending is a pretty dark variant of Stinger, why are you asking?
The Simpsons episode I Love Lisa was a Valentine's and President's Day episode, yet it begins and ends with the KBBL disc jockeys playing the song 'Monster Mash'.
The South Park episode "Coon 2: Hindsight" (the first of a trilogy of episodes) began with Cartman/the Coon criticizing Bradley/Mintberry Crunch's identity ("Maybe you need to add something else to the mintberry crunch part of your costume." "Like milk?" "No, not like milk!"), along with this conversation with Butters/Professor Chaos:
Cartman: You aren't going anywhere, Chaos! Butters: Yeah, but you only gave me this bucket to poop in and it's full now. And I ain't got nothin' to eat. Cartman: You've got poop, don'tcha?
The last episode of the trilogy, "Coon vs. Coon & Friends", begins with the group criticizing Mintberry Crunch, and features this converation near the end
Kyle: You're not going anywhere for a long time! Cartman: This is inhumane! There's a big bicket with Butters' poop in here, and there's nothing to eat! Stan: Ya got poop, don't ya?
The SWAT Kats episode "Bride of the Pastmaster" used this. The episode begins with the Turbokat flying towards an oil tanker under attack by a sea monster. The episode ends with the Turbokat, freshly returned from its adventures in time, flying towards an oil tanker under attack by a sea monster. Razor even invokes this. "Isn't this where we came in?"
Tiny Toon Adventures begins its first episode with Bugs Bunny narrating the episode and concludes its final episode with him making a brief one-liner.
The Tom and Jerry cartoon "Blue Cat Blues" begins and ends with Tom depressed over losing the white cat to Butch leading him to attempt to kill himself by being run over by a train. In that same end, Jerry faces the same fate when he loses his girl to another mouse and joins along with him.
The very first shot in Transformers: Beast Machines is a flower growing through a crack. In the very last shot, the camera zooms in on the same flower.
Another one occurs if Beast Wars and Beast Machines are taken as a single series. Cheetor gets the very first line of Beast Wars and the very last of Beast Machines, reflecting his Character Arc from rookie kid to wise leader.
In Trollz, episode 2 has everyone saving Amethyst from falling into a pit. The last episode has them saving her from falling into a volcano.
Young Justice episode "Insecurity" began and ended with the scene taking place at night between a father and a daughter, with the father calling his daughter by a term of endearment "baby girl". While Mr. Jones in the beginning likely sincerely meant it as a term of affection to his daughter, Sportsmaster used the term as straight up manipulation, attempting to regress Artemis back to when he could dominate her to his will.
The first episodes of both seasons included a scene of the Justice League flying in to surround the awed teen heroes with a majestic piece of music, which the creators specifically referred to as being like the gods descending from Mount Olympus. The final episode of the series has a scene of several Leaguers being surrounded by the team flying in, to the same music. It's hurt somewhat in that the majority of the team can't fly and are being carried by the Super-Cycle, so that there's barely enough airborne members to properly duplicate the "surrounding with awe" effect.
Kid Flash makes his first appearance in the pilot episode running circles with The Flash. His death scene in the series finale has him doing the same.