The episode "Girlz, Tenshin!" ("Trading Faces" in the English dub) of Demashita! Powerpuff Girls Z has this happen to the three girls courtesy of Fuzzy Lumpkins, resulting in each girl having to pretend to be the other.
Kochikame has a rare Double Subversion. Ryotsu wishes he could swap his body with his rich, handsome and skillful underling Nakagawa. The next day there's an accident that involves Ryotsu and Nakagawa banging their heads. All seems set for a Freaky Friday Flip Episode...except it's not. The Genre Savvy Ryotsu tried to make it look as if the Freaky Friday Flip had really happened, hid Nakagawa's body in a secret medical facility and assumed his identity, power and fortune, knowing that everyone would automatically believe such a strange event. Then later the trope is played straight when the resident Mad Scientist tries to "restore" Ryotsu and Nakagawa to their original bodies, with a machine that explodes and produces a CHAIN FREAKY FRIDAY FLIP (Terai with Nakagawa, Nakagawa with the Chief, the Chief with Akimoto, Akimoto with Ryotsu, Ryotsu with a nearby cat, the cat with the Mad Scientist and the Mad Scientist with Terai). Yeah. Ryotsu comments that Nakagawa's life is not easy, but the aesop is never really delivered.
Another time, Ryotsu and Reiko had their bodies switched. It began with the mad scientist inventing a body switching machine shaped like a purikura photo booth. Reiko, unaware of its purpose, took a picture together with Ryotsu. By morning, their bodies switched. The whole episode deals with adjusting their lifestyle and playing their roles. Ryotsu has to attend Reiko's important meeting. And even worse, Reiko is a target of a few dangerous kidnappers who later kidnap Ryotsu in Reiko's body. Both of their bodies switch back during the police holdup, scaring the kidnappers when Ryotsu gets reverted back to himself.
In Excel Saga, the two main characters, Excel and Hayatt, swap bodies in the Grand Finale episode, which took everything in the series to date to the extreme, which meant they both found "themselves" to be attractive and overt lesbianism ensued. It was the final episode, so they had absolutely nothing to lose.
Murder Princess is about a seasoned bounty hunter getting switched with a demure young princess. Apparently, some very powerful enemies thought she would be easy prey. They're in for the shock of their lives.
It might be worth noting in this example, their voices don't switch, although their accents do.
In the American version, which doesn't include accents, the voices DO switch.
The Latin-American Spanish dub has Syaoran and Kero switching both. Kero's accent isn't halfway as marked as in the Japanese version, but Syaoran!Kero's speech patterns remain.
In Haré+Guu, Guu does this to Haré and Dr. Clive as a "birthday present". They both use the body's voices when speaking, but use their own voices when thinking.
Pokémon Ranger and the Temple of the Sea. The newly hatched Pokémon Manaphy does this twice: switching Team Rocket's minds among the three of them, and switching the minds of Ash Ketchum and Jack Walker (the eponymous Pokémon Ranger).
Crayon Shin-chan did a child/parent switch between Shin and Misae ("Mitzi" in FUNimation's Gag Dub) and they didn't even switch voices (Goes for the dub as well). Much Hilarity Ensues, including Misae doing the beloved ass dance.
In Urusei Yatsura, chapter 72 of the manga features an Ataru ↔ Ten swap followed by a Cherry ↔ Ten swap, done by earmuffs. This chapter was adapted into episode 24 of the anime, which diverges from the original story partway through and ends up with a dappya monster ↔ Lum swap as well as a 9-way (!) swap: Sakura → Ten → Cherry → a cat → Mr. Moroboshi → Shinobu → Ataru → Mrs. Moroboshi → Megane → Sakura (where "A → B" means "A's mind controls B's body").
Asatte No Houkou does this with a twist. The characters switch ages rather than bodies, and they do it in order to learn more about themselves, rather than to learn about each other.
It probably derives from that Sailor Moon Dream Arc part where Usagi and Chibi-Usa switch ages.
After seeing the preview for the episode, many people thought she would have to transform while in his body. It turned out to be the reverse, him transforming in her body with her in his body assisting.
A similar situation occurs in episode 8 of Smile Pretty Cure!, with Miyuki and Candy switching places. Unlike Inori and Tart, though, Miyuki does transform while in Candy's body. And it is HILARIOUS.
A weird example in Birdy the Mighty DECODE: Tsutomu and Birdy were, of course, already Sharing a Body, but said body's appearance changed depending on who was in control at the moment... until a nasty run-in with a reality-warping BFG led to Tsutomu waking up in Birdy's body, with Birdy's mind apparently MIA.
An episode in the second season of Galaxy Angel features a piece of Lost Technology that switches the minds/bodies of members of the Angel Brigade. Impressively, the VAs stay with the same body, but mimic the speech characteristics of the actual character they are voicing. Even the elderly male Commander. Even more impressive is that the characters swap bodies several times in this episode.
In a Gintama one-shot story, Gintoki wakes up to find he's switched bodies with Sadaharu. After failing to get any of his friends to notice the change, he goes to sleep... and wakes up to find he's now inhabiting Shinpachi's glasses.
This forms the basis for the first episode in the Shakugan No Shana S OVA series. A bit of Applied Phlebotinum causes Yuuji and Shana to switch bodies, which makes for some awkward moments as they try to swap back and happen to run into pretty much the entire cast.
Urashiman and Jitanda swap in episode 21 of Future Police Urashiman because of botched shock therapy to restore their memories.
Done in one of the Fairy TailFiller episodes. Natsu, the man-beast, swaps with Chivalrous Pervert Loke. Gray, who subconsciously strips, swaps with The Chick Lucy. Erza, the strongest main character, swaps with Happy, the blue cat who can sprout wings. Naturally, Erza spends the whole episode switching between cranky, freaking out, and depressed. Lucy also has to foil several attempts of Gray's to strip. And they can't control each other's magic, leading to Lucy drooling ice and Loke spitting out fire while trying to ask out different girls. Happy is pretty much the only one of them to enjoy being in the new body, constantly playing with boobs and experimenting with outfit transformations. By the end, Lucy and Gray manage to change back... but not only are the OTHER main characters switched, everyone in the guild ends up switched as well!
In the last episode of the anime of Kampfer the entrails animals switch bodies with their respective owners. The stuffed animals resolve that "Life... is fabulous!"
Happens in one of the visual novels for Haruhi Suzumiya, with Yuki and Mikuru due to Haruhi. Their seiyuu do not swap; however, they do take a crack at voicing each other using the right personality, resulting in a scary, deadpan-sounding Yuko Goto and a moe moe Minori Chihara.
In Masakazu Katsura's short story "Woman in the man", the tomboyish Hazumi and the wussy Tsuyomaru switch bodies after an accident in the gym owned by Tsuyomaru's parents.
In an episode of Tanoshii Moomin Ikka: Bouken Nikki Moomin and Stinky bonk their heads together and switch bodies. Over the episode, Moomin realizes how Stinky has no friends and Stinky has fun messing up Moomin's life.
In Dragon Ball Z, Captain Ginyu has the power to switch bodies with anyone, which he does with Goku. Eventually however, it backfires on him when he tries to take Vegeta's body and ends up in a frog's instead, rendering him harmless as his power requires the use of his voice. In the filler Bulma unwittingly gives the frog Captain Ginyu a speech device that allows him to speak. He switches bodies with her. He attempts to switch again with Piccolo but Krillian figures it and and throws the frog in his way causing him to switch back to the frog's body (he no longer has the speech device and is not able to switch anymore).
A rather odd version occurs in Sumire 16 Sai owing to the fact that the characters in question were literal puppets. While this would normally be incredibly easy to reverse, one of the puppeteers ran with the trope, much to the dismay of the other (and amusement of the audience, of course).
In Jojos Bizarre Adventure, "Vento Auro", this makes up the Climax, thanks to Silver Chariot Requiem's ability doing this to everyone in Rome.
Played out several times in Doraemon, usually with Nobita trading places with Shizuka. Needless to say, it turns out that Nobi is just as big a loser no matter whose body he's wearing. Worse still, Shizuka decides she actually likes being a boy and refuses to give Nobita his body back. She only relents around bathtime, when she suddenly realizes exactly what Nobi will see whenever "he" removes "her" clothing.
Quite a few people try to swap their mechanical bodies with Tetsuro's human body in Galaxy Express 999. At least one of them succeeds, even if only for a short while.
In Petshop of Horrors, D lets a mermaid switch bodies with him for a while, so that she can go to the shore to contact her human boyfriend again. Hilarity Ensues when Leon, who doesn't know what's going on, finds a seemingly mute D and a hot naked mermaid.
In All Around Type Moon Kohaku uses a device for make Saber, Arcueid and Shiki swap bodies. Taken up to the eleven when more members of the Type Moon series appear and Kohaku "reverses" the body swap.
In the Punk Hazard arc of One Piece, this happens to Sanji, Nami, Chopper and Franky, courtesy of Trafalgar Law's Ope-Ope Fruiti powers.
Soon after, this happens to Tashigi and Smoker. Seeing Tashigi look all innocent in Smoker's body and Smoker look all badass in Tashigi's body is nothing short of fucking hilarious.
In To Love-Ru Rito and Haruna swap bodies after touching an invention by Lala.
In Sket Dance on the school trip Bossun and Himeko accidentally drink some pills that switch their minds. What makes it hilarious is that Himeko (in Bossun's body) insists that Bossun must not touch any intimate part of her body (which he now possesses). Which means that all delicate operations on that original body of her (like wiping the ass or, what a horror, bathing) should be done by Himeko herself (who is now in Bossun's body, remember!). This leads to some scenes which, taken out of context, would be considered very perverse.
Later explained it isn't Yamada the one who can switch bodies, the one who has the power is Urara Shiraishi. He just copies her ability when he kisses her.
Episode 13 of Miracle Girls has a swap between identical twins. The trope is played utterly straight, with each of them having to pretend to be the one whose body she's in, even though they could just pull a Twin Switch using a couple of wigs and look exactly like themselves anyway.