The most infamous anime Bowdlerization of the modern era (prior to 4Kids) was, without a doubt, the original dub of Sailor Moon. The numerous visual cuts and dialogue edits made by DiC/Cloverway/Optimum Production to the series are legendary, and have certainly contributed to the series' stay in licensing hell until Viz picked it up and redubbed it.
Shots of Usagi in the bath were edited to remove her cleavage, as were the clips of the girls transforming to remove the outlines of their breasts and buttocks.
While one of the most infamous dialogue changes was Sailor Uranus and Sailor Neptune being changed from Schoolgirl Lesbians to "cousins", the edits rarely extended to any of the original visual innuendomaking them incestuous lesbians, which is hardly new to anime but probably wasn't Cloverway/Optimum's intention. Parody fanart here.◊
In Sailor Moon S, Makoto/Lita implied that she had a mom who was allergic to cats (in the original, her parents died in a plane accident — which is the reason why Makoto has a fear of airplanes and lives alone).
Rei's grandfather was originally very lecherous (he still is in the dubbed version, but it was toned down in some places). New dialogue helped here, but in one episode from Sailor Moon R, Rei shows Grampa a magazine ad. The dub claims it's an ad for ladies' wrestling lessons at his dojo (that Grampa accidentally made into a two-page spread instead of a one-inch ad with Grampa freaking out over how much a two-page spread is going to set him back), but it originally was a warning for girls to look out for a dirty old man in the neighborhood. Noted in this parody fanart here.◊
Little things like that were always being changed in the DiC dub (and, to a lesser extent, the Cloverway dubs); in one episode, when chasing Zoisite (who is about to steal a Rainbow Crystal supposedly inside a little girl) into a narrow alley, Sailor Moon, Mercury, and Jupiter cram themselves in and are unable to move. Sailor Mercury attempts her bubble attack, which requires a certain awkward pose, and trips, leaving her bent forward with her backside in the air, unable to actually fall forward. Jupiter, behind her and much taller, has a close-up view of her posteriorand she blushes and stares, wide-eyed, as Mercury struggles to stand up. In some airings, Mercury fell half-way down but not completely and Lita's blushing was digitally removed from her cheeks.
Several episodes that aired in the U.S. feature Usagi/Serena going to a party and proceeding to get "sick" because she drank too much "juice". By the third such time, they weren't even trying.
And of course, in the original, Makoto says that she should get a certain role in a play because she has the largest breasts; in the dub, Lita says it's because she has the most talent. The shot of Lita thrusting her chest forward, however, was not cut — even the boing sound effect was left in — so her meaning is still quite obvious and the end result was that the fans adopted "talent" as an Unusual Euphemism.
The final two episodes of Season 1 were combined into a single episode in the dub because the other Sailor Guardians died in it, and it reportedly made little girls in Japan so upset that they wanted to stay home from school due to it. However, one scene featuring the ghosts of the Guardians showed up in the Sailor Says for that episode.
Most of the fight between Prince Endymion and Sailor Moon was edited to be less violent. Scenes of him brutally kicking Usagi, electrocuting her, and choking her were completely cut out of the first dub. Even a scene where Endymion swings his sword and misses, due to her dodging out of the way, were deemed too violent. The ensuing fight with Queen Beryl was also edited in such a way to simply have Darien becoming injured after shielding Sailor Moon from a crystal projectile thrown at both of them, whereas in the original version, it killed him.
Fish-Eye is gay and sometimes changes gender to fit whatever disguise he's using that episode. In the dub, they just made him a girl just like with Zoisite. But then one episode has "her" in a Shirtless Scene; later airings would have it edited to a close-up on Fish-Eye's face, but in its first run, there were no edits because it was an ordinary male chest.
Let us not forget that they dropped episode 42 entirely. Apparently Sailor V being Sailor Venus was just too confusing for little kids so they dropped Minako's main characterization episode wholesale. They also dropped 2, 5, 6 and 20 but those were less character critical.
Both times Usagi is slapped in the original series, when Rei slaps a hysterical Usagi who is suffering from a massive Heroic BSoD and when Ami slaps Usagi after Makoto is killed at the end of the first series are removed, as well as Chibi-Usa's spankings.
The Sailor Moon manga received a few edits between the anime and manga. For example, in the manga the Starlights are crossdressing instead of being genderswapped on Earth. This was reportedly because of controversy with Uranus and Neptune in previous seasons. Naoko Takeuchi was understandably not pleased with this edit.
A similar thing was done with the Italian dub of Sailor Moon. In the fifth season, Sailor Stars, there are the Sailor Starlights — women who disguised themselves as men on Earth and revert to their female form when transformed. Since Seiya has a crush on Usagi throughout the season and to prevent a Uranus-Neptune thing again, they turned the Three Lights into real men who call their twin sisters from their homeplanet to take their place in battle. This actually got the fifth season banned in Italy for just over a decade when the Italian localization infamously tried the exact same thing in an epic overreaction to an inadvisable remark by a local "psychiatrist" about "Sailor Moon [making] little boys gay".