In episode 7 of the anime Hanasaku Iroha, Ohana hums the opening theme in the bath.
In the original Japanese version of the first season of Sailor Moon, its theme song, "Moonlight Densetsu", is apparently a current hit. It is sung several times by different characters, including once as a duet in a talent show. (It should probably be noted that the "fighting evil by moonlight" lyrics were created for the North American dub; the original is actually about finding one's "miracle romance".) Interestingly, a slow version of the same tune is played by the star-shaped locket in the first season — this locket is also present in a flashback to the Moon Kingdom, which existed in the distant past. Perhaps the song is older than it seems...
Although it's not the show's theme tune, the anime Full Metal Panic! regularly uses a variation of the theme song from The A-Team as background music. In the follow-up series Full Metal Panic Fumoffu, the song is also used as the main character's cellphone ringtone, and one other character remarks how it sounds "just like the theme song of one of those old American TV series".
In the 2005 series of the animeAh! My Goddess, Belldandy and Holy Bell sing a haunting rendition of the theme song, Open Your Mind, as part of a magic spell. In the second season she sings it again during a talent contest with Sayoko, who sings the first season ending theme.
Similarly, during the Festival Episode of Love Hina, Seta asks Haruka (voiced by Megumi Hayashibara, who recorded the theme) to sing for him "just like she used to." She then begins singing a slow, almost melancholy, version of the very hyper theme song. Most of the other Hinata girls scattered throughout the festival each join in, until there is a chorus of voices singing on the final line.
Characters in Martian Successor Nadesico frequently sing snatches of the opening theme, most often just the title line "You Get to Burning" — and usually not very well. At one point Erina even chastises Yurika for messing up the lyrics.
And in the "Idol Singer" episode, Yurika sings an expanded version of the ending theme.
In the Christmas episode, Seiya makes up Christmas-related lyrics to sing to the tune of the opening theme.
Abenobashi Mahou Shoutengai: In a world that may or may not be the original one from which they come, Sasshi and Arumi stand in the shopping arcade proper and look around while the closing theme of the show plays, muzak-style, over the PA system.
In Keroro Gunsou, while doing chores around the house, Sgt. Keroro sometimes sings his own version of the show's closing theme.
Another episode had Sumomo singing a few bars of the show's theme.
Another one had the first ending as Fuyuki's ringtone.
And another one had the first season's summer-only Dance Festival ending used for a dance rehearsal, about two years after the fact.
Even the manga gets into the act; the first chapter of volume 19 features Keroro singing one of the closing themes from the anime at a karaoke club.
In an episode of Princess Princess, the "princesses" and student council go for karaoke to train for the school festival. The Student Council President begins to sing the opening Anime Theme Song in one room, whereupon the "princesses" retreat to a different room by themselves... and sing the ending theme. Then, when the actual concert comes, they sing the theme to Cutey Honey.
In Nana, the Black Stones' first hit song is the OP for the series, and a hit single from their chief rival band is the series ED. Both songs show up several times in the show itself.
A quieter, softer version of the theme for WORKING!! plays as the restaurant's background music.
In an episode of Rockman EXE (Mega Man NT Warrior outside Japan), the protagonist's mother is humming the opening notes (from when they start singing) of the theme song.
The sequel series, Ryuusei no Rockman, reuses the opening as the first song a popstar composes on her own after angsting about only singing what's given to her. In the first episode she sings it in, she uses it to distract The Dragon Gemini Spark from a battle. Yes, he/they (don't ask) stand there and stare at her for the entire ninety seconds the song goes on. So does Rockman, actually, not attacking as per the diversion she intended the song for until the last couple seconds of it.
Also done in Ryuusei no RockMan Tribe. The song Misora sings at the concert in the last episode is the theme song, "Kizuna Wave." The animators even used footage from the opening (although that may have because the ending was rushed to completion).
In one episode of Rockman EXE Axess Netto hums the ending theme of that series while he's in the shower.
The opening of the anime series Gankutsuou (We Were Lovers by Jean-Jacques Burnel) appears in-show as the song one of the characters composes and plays on the piano in several occasions.
Re:Cutie Honey plays with this by having a villain sing the theme song... but replacing the lyrics about how beautiful Cutie Honey is with how much she hates Cutie Honey. She even gets the mooks into the action.
The Pretty Cure franchise does this way too many times:
In one of the later episodes of Futari Wa Pretty Cure, the choir club has to find a song to sing... and they pick the show's ending theme.
And they even dubbed the song in the English Dub of Pretty Cure instead of replacing it, although the ending theme was an instrumental of "Together We Are Pretty Cure", the dub's opening theme.
The same theme (Get You! Love Love?) would occasionally be hummed by a recurring character, even once after the show became Futari Wa Pretty Cure Max Heart and the ending theme was replaced with a new one, named MuriMuri? Ariai! INJanai!?
In episode 12 of Max Heart, Honoka, Hikari, and Akane sing the the first verse of the show's ending theme, Murimuri!? Ariari!! IN jana~i?! (Impossible!? Possible!! Isn't it?), while driving to the Nadesico Ranch Festival.
Fresh Pretty Cure's first ending is apparently part of Trinity's song list (played in the first episode). The second ending is played during a dance contest in the final episode.
The orchestral version of You Make Me Happy! played during the episode of the next season when Eas dies.
Heartcatch Pretty Cure gets into the act in episode 41, using both the opening and second ending themes for the respective parts of a puppet show.
In the Pretty Cure All Stars movies, when the respective Pretty Cure teams come on during the climax of the movie, their theme songs played.
In Smile Pretty Cure, a instrumental, slow version of Yay! Yay! Yay! is background music.
Elfen Lied's theme, "Lilium," was frequently used within the show — Kouta had a music box which played the tune, and was playing it when he and Lucy met as children. In the present, the theme was used to allude to their former relationship, the memories of which Kouta had suppressed after Lucy killed his family. For instance, it made Nyuu very upset, even though she didn't know why, and even caused her to revert to Lucy.
Lucia's music box in Mermaid Melody Pichi Pichi Pitch plays the show's first ending theme, and sometimes the episode titles and important lines are actually song titles (usually "Yume no sono saki e"). Being a series that incorporates music all through, there are too many instances of characters singing their own songs to list.
Death Note has Nightmare's "Alumina", the first ending tune, as the ringtone on Matsuda's mobile phone, and the first opening tune on Misa's.
Also "Alumina" can be heard on Misa's laptop in episode 13. Still it goes largely unnoticed by most fans.
Episode ten of Paranoia Agent, in which a frantic victim accidentally turns on his car radio and the show's opening theme song plays.
The Lupin III movie Crisis in Tokyo features Lupin whistling the franchise's theme song.
There's also Fujiko humming it while driving a truck in the series proper.
In the TV special "Stolin Lupin", Lupin's ringtone played the theme song.
One dub episode of Yu-Gi-Oh! GX has Jaden singing part of the theme song.
Another dub episode has Fubuki/Atticus singing (badly) a Parody version of the theme song. "Rock on! Get your rock on! Everybody rock now!"
In the original version of the original series, it happens too, with Anzu's ringtone being the second season opening song.
The Yu-Gi-Oh! 5Ds dub does this twice. At one point, the hyperactive Cloud Cuckoolander scientist is caught singing the theme. Yusei also had it playing on a music player in one episode, while fixing his Duel Runner.
The ending theme of Rurouni Kenshin, sung by the voice actor of Sanosuke, was discontinued; in the next episode, Sanosuke is walking down a street and singing it.
In the DNAOVA, Karin Aoi and Junta's mother sing karaoke, performing the series's closing and opening themes respectively.
This is a real world concert Suzumiya Haruhi no Gekisō that the characters 'attended'. The 'person' singing on stage is Aya Hirano, credited as such (she is also the VA of Konata and Haruhi) and is a fairly good likeness of the actress.
The ending themes for Lucky Star up to episode twelve are often themes to other (non-Kyoto Animation) series, anime or otherwise. The others are general popular tunes.
And yes, Lucky Star's own theme makes an appearance, hummed by one of the girls in episode 6.
And in episode 24, when the Dancing Theme is animated in full. (Well, full shortened version, anyway.) In the same episode, Minoru is interrupted by his ringtone, which is his own version of "Koi no Mikuru Densetsu"(one of the endings).
The Arcus Prima in Simoun has a phonograph-like machine which is often heard playing background music from elsewhere in the series. It almost escapes this trope, but it finally plays one of the themes (the end theme) in episode 25.
In one episode of Ai Yori Aoshi, Kaoru of all people sings karaoke to the end theme. A different song (sung by Tina) plays over that episode's credits, perhaps indicating some kind of theme conservation law. Aoi is also humming the opening theme at the beginning of episode 15.
The vocal version of the aptly named instrumental track "Nagisa" from the CLANNAD visual novel, "Dango Daikazoku", is used as the first ending for the anime series, and is sung in the second episode by Nagisa herself. It is also said to be Nagisa's favorite song. Also, as evidence of how much his girlfriend is rubbing off on him, Tomoya whistles it in the third episode of the After Story. It makes several other appearances throughout the anime, too.
In The Movie, Nagisa sings the song and it is also used as background music.
The anime also contains several musics based on the opening theme, "Cruel Angel's Thesis." Also note that in an interesting reversal, the ending theme of the movie Death and Rebirth ("Thanatos — If I Can't Be Yours") was based on a music from the original anime.
The Hot Springs Episode in Maburaho has Kuriko listening to the theme song on her portable music device on the train.
Alicia from ARIA at one time hums the opening tune of the series while lighting some candles in her home.
Inverted in the second Digimon Tamersmovie. Parasimon forces Ruki's memories of her father to the surface, and of a song she used to sing for him—which just so happens to the movie's ending song. While Ruki's seiyuu recorded the full song (which was later released on CD), the version over the end credits was performed by Ai Maeda, the regular singer for nearly all of the franchise's ending songs. Later, during her birthday party, Xiaochun and Ruki's mother sing karaoke of the series' opening and first ending, "The Biggest Dreamer" and "My Tomorrow".
While we're at Tamers, an interesting one: Ritsuko's ringtone is Ravel's Boléro. While technically not originally a Digimon song, the track was part of Digimon Adventure's soundtrack, usually played within the context of the real world.
In Digimon Adventure, the song Mimi sang to wake TonosamaGekomon was the first ending, I Wish. Mimi was also voiced by Ai Maeda, so they just had to use the prerecorded audio until he woke up.
The Digimon Xros Warsmanga got in on this, with Shoutmon singing the anime's opening theme at the end. He also sing's Adventure's opening.
Hideaki Asaba from Kare Kano is seen (and heard) listening to the series' opening theme, Tenshi no yubikiri, in one of the later episodes of the anime.
An early episode of Ultra Maniac involves the characters going to a karaoke bar and singing snippets of the opening and ending themes as duets. Singable lyrics were written for the dub. Nina, a transfer from the Magic Kingdom, sings a song from Doraemon, since it's the only one she knows.
In one episode of The Vision of Escaflowne, a character finds and plays a music box. The song it plays is "Yakusoku wa Iranai", the show's opening theme.
Although not quite as blatant, Macross Plus evokes this trope with "Voices," the first and last song heard in the OVA, sung by Myung at various points, and used in instrumental form as her leitmotif.
In an episode of Ranma ½, some characters perform part of the first season opening song for karaoke.
One of the opening songs also appears in a TV show that Ranma is watching.
It goes further than that: in the Christmas EpisodeOAV, the characters that would compose the DoCo supergroup (Akane, female Ranma, Kasumi, Nabiki, and Shampoo) perform the "Equal Romance" ending theme for the benefit of their party guests. Additionally, an entire two-part OAV, Nettou Uta Gassen, consists of the entire cast performing a multitude of songs in-character.
After a particular denial of a normal body for Ranma, he closes the episode in girl form, sadly singing the refrain to that season's end theme: "Don't cry, China Boy..."
Another instance of this occurs in anime season 3, episode 18. Ling-Ling and Lung-Lung use weaponized music that forces the opponents to dance while they are blasted with fire. The music playing is the first opening theme and it seems that we never hear the music that's actually playing. When Ranma defeats Ling-Ling and Lung-Lung, the stereo lands on a tree. The stereo opens and the music immediately stops playing, implying that the music Ling-Ling and Lung-Lung used was the first opening theme after all.
Similarly, in Mezzo DSA, Mikura brings her karaoke machine on a car ride (to Harada's annoyance) and sings the theme song. This would be fine if she didn't sing it all the way through... more than once. You'll never see a more obvious "rake scene" in anime.
The bar in Tokyo where Lucy meets Akagi some time after Saeko's death in FLAG has a lounge singer singing the show's ED song, Lights. The singer herself looks suspiciously like Eri Nobuchika, the real-life singer of the ending theme, and the bar itself is named Lights.
Top wo Nerae!2 Diebuster episode 4 has a moment where Nono hums the beginning of "Active Heart," the opening of Gun Buster.
Monster uses its theme song as background music at restaurants, dance clubs, and such. The sneaky part is that it's played cabaret-style — so slow and laid-back that you can easily fail to recognize it.
Hell Girl has used at least two of its themes as ringtones. Also noteworthy: SNoW, who sings the OP of seasons one and two, has a cameo on an advertisement at the end of Futakomori's theme.
In the first series of Dragon Ball (at least in the French dub, which had a different opening) Goku hums the Japanese theme song before kicking ass.
Launch briefly does the same during Goku's second fight with Piccolo Daimo.
Tayutama's ninth episode has a brief Karaoke Box session that has characters singing the anime's opening and ending, as well as the opening of the fandisc of the Visual Novel it was based on.
Cromartie High School plays with this in Episode 3: 'Hmm hmm hm-hm-hmm hmm-hmm hm-hm-hm-hmmm-hm-hm' It's "Ningen Nante", another song by the maker of the show's theme. You'd think it was related to the show, but it's actually Subliminal Advertising.
The show uses three different credits songs, and all of them get a cameo at some point:
The first ending credits tune gets played on a cellphone, who is Mechazawa's little brother.
When a one-off character listens to his CD-player, you can hear the second tune playing right before it breaks.
Kamiyama sings part of the lyrics for the third tune (which appears to be the rock version of the school's Alma Mater Song) 14 episodes before it gets used.
The Japanese version of the previously-banned-then-not-anymore-and-then-again-yes episode, the Beach Episode, has Koujiro (James) exclaiming that he and Musashi (Jessie) will "go through the fire and through the water". The sentence is part of the original opening's lyrics.
Any time Brock has to sing, he will always sing "Takeshi's Paradise" (Takeshi being Brock's name in Japan), one of the end themes in the Johto arc; apparently it's the only song he knows.
And other OP's and EP's have been used as background music too, but most of the time this is lost in the dubs.
The first scene of episode 69 of Shugo Chara! has Kusukusu humming the show's opening theme.
In Duel Masters, after Knight is accosted by a mysterious cloaked servant of the Temple (who happens to be Mimi), he leaves wondering what the other person could possibly be thinking. Her thoughts are revealed afterward. "Who's the kid with the spiky hair? Shobu!"
In an episode of Suzuka, a very bored Hatari is left alone in a karaoke parlor and is shown (barely) singing part of the show's opening theme.
In episode 14 of Sasami: Magical Girls Club, Itoki sings both the opening theme and the first closing theme at a karaoke parlor. The scene begins with her singing the opening theme, then later in the same scene she starts singing the original ending theme and the screen behind her even shows a glimpse of the original ending credits.
Taken to ridiculous levels in Hime-chan No Ribbon. Apparently, "Egao no Genki" (the series' opening) and the band that performs it, SMAP, is extremely popular in Hime-chan's world — in one episode, Hime-chan pretends to have invited SMAP to a school event to save the drama club's reputation by turning into the band members and walking out on stage one at a time, there was almost a scandal when Hibino was caught hugging Hime-chan disguised as one of the band members, and the song pops up all over the place.
If you carefully listen in Episode 31 of the Kirbyanime, Mike Kirby will be singing to the ending theme of Japanese version, "Kihon wa Maru". Kirby sings it in "Kirbyese" though (his "Poyo" sounds), though if you listen carefully you can hear him say "Kirby" and "Dedede" at the appropriate points in the song.
In another episode of the anime, Escargon sings a song about how much he loves (in a platonic way, not like that) King Dedede, set to the tune of the first opening, Kirby March.
During battles with some "demon beasts", one of the songs that plays contains a remix of part of the Japanese theme song (which made it into the game Kirby Air Ride as the Kirby Melee music).
Outlaw Star's opening theme is played by a gigantic advertising spaceship in the episode "Final Countdown." The first ending theme also appears twice, sung by Melfina.
In You're Under Arrest!, the episode in which Sena is introduced has the first opening theme, 100 MPH no Yuuki, play on the radio.
Natsumi also sings part of the second opening theme in one episode.
An episode of Black Jack (I'm not sure which one.) had a woman singing the second closing theme song on stage.
In a episode of Buso Renkin, Hideyuki Okakura hums the theme song.
In episode 47, Little Italy interrupts Austria's piano recital while singing Maru Kaite Chikyuu. In the middle of it, Italy's voice changes, and Austria not realizes that Italy hit puberty, he found out that Italy wasn't female.
At the end of World Series episode 34, Italy hums Hatefutte Parade while spying until Germany tells him to stop.
In Peach Girl, Momo and Sae's ring tone is an instrumental version of the opening theme.
In (one) Bizarro Episode of Ergo Proxy, Vincent is trapped on a game show, and one question is to name the composer of a song. Then the theme tune plays, and we find out that Vincent guessed correctly. The Fourth Wall was never the same again.
In the second season of Strike Witches, Shirley hums the first season's ED.
In one of the early episodes of the dub of the Witchblade anime, a character hums part of the chorus of XTC, the show's first opening.
In Touhou: A Summer Day's Dream, Suika hums a snippet of the opening theme as she helps Reimu clean up the shrine.
In episode 8 of Slayers Evolution-R, a scene opens up with Gourry humming along to the soundtrack, only to be scolded by Xelgadis.
At one point, Ryo Saeba whistles the beginning bars of Ai yo Kienaide, only to be cut off when confronted with a beautiful lady.
Excel Saga takes this to the next level, with the song being performed by animated representations of the voice actresses who normally sing it, themselves being dressed in the distinctive outfits of the main characters and being derided as knockoffs thereof.
The English dub of Burst Angel has the ending theme recited as a poem in one episode.
In one episode of Windy Tales, Nao sings the ending theme song as part of an audition.
When the cast of Yumekui Merry goes to a karaoke bar, we hear someone down the hall performing the show's theme song, and doing a remarkable job of sounding like the original singer.
The 2007 Tamagotchi movie uses the ending theme as Tanpopo's ringtone. This is done twice: at the beginning of the movie, and at the end of the movie, when the Tamagotchi cast uses the key to send Tanpopo back to the same time she came to the Tamagotchi World.
A fairly subtle one in Cardcaptor Sakura has a random woman humming the second season opening as she walks to the mailbox.
Guilty Crown has Inori singing the first ending theme in-series to combat the effects of the Apocalypse Virus that had been activated by a crystal resonance. She also sings "Euterpe," the song that the series began with (but isn't the official opening theme), to herself when she's lonely... and also sings it at the Cultural Festival the high school puts together.
Rin in Kodomo No Jikan hums the opening theme, "Rettsu! Ohime-sama Dakko" - basically, "Let's! Carry me like a princess" - to herself in the bath. An earlier scene plays on the theme's title, where Rin asks her teacher to carry her like a princess.
In Magical Princess Minky Momo's second series, the episode "Momo and Momo" has two instances of this. First, the intro to the first series plays when the magical dresser explains the story of the original Minky Momo. Later, the original Momo sings the same song when cleaning a chimney. This happened in another episode involving a "Fenarinarsa satellite", where the original Momo sings it while watching the filming of the satellite before she talks to the other Momo.
Anpanman has the theme song, "Anpanman's March", sung by the town's children a few times when they go on class trips. Also, Tendonman and Katsudonman's in-show songs are modified version of their image songs, and they sing it every time they're in the show (Kamameshidon's song is completely different from his image song).
An odd variation: In Tenchi Universe, when Mihoshi and Kiyone go to the karaoke club, it's apparent that they sing the song "Sleeping Beauty on the Balcony", the theme to the special "Space Police Mihoshi's Space Adventure", the special that introduces Kiyone.
In the manga No Need For Tenchi, one incident has Katsuhito learning that there was a dangerous wolf out there and that the others, who were looking for Sasami, were still out there. He stops when he finds out the next song on the radio is Ai Orikasa's "The Moon Tragedy" (better known here as "The Lonely Moon"), which was the OVA's second ending theme.
Two episodes of Kotoura-san include scenes in a karaoke box: episode three has Haruka singing the opening theme, while episode twelve has her singing the ending theme.