In I, Robot, a scene that showed in the European version did not show in the US version. It was a full body nudity shower scene and the point was to show you how extensive his robotic parts were. They had to find some other means to explain that to the audience in the US and it wasn't even a sexual scene. Just full nudity (of Will Smith, to be clear).
"Tentacle beasts" in, I think, Japan can do all kinds of sexual stuff that would be outrageous in the US and not shown here. I am not super familiar, so can't really elaborate.
We also have a long history of using "coded messages" to talk about racial stuff in the US. When Elvis first aired, he sounded so much like a Black musician compared to what was the norm for music at the time that they would talk about what high school he was from as code for "This is a White guy" because segregation was a thing, so naming his high school was signaling his race.
We have a history of censoring LGBTQ topics. I saw something once where they showed a deleted scene from an old black and white film about Roman history and the scene was a coded message about whether someone was gay or bisexual or something. They used some euphemism or other and it was considered too much and got cut.
Violence. I have become a fan of things that are careful in how they show violence, showing just enough to know something bad happened while sidestepping unnecessary gore. I think that's generally a good thing, but it is a form of censorship nonetheless.
Are you sure this is true, and not an apocryphal story? I've seen the German and US version of the movie, and they are identical. There is a nude shower scene in both, and Will Smith uses has hand to cover his groin.
I've seen two interviews, one where he said his penis was so big they had to tape it down, and a second where it was so big, they had to CGI it out because it was distracting. They both seem like they may have been self serving jokes that got evolved into the "full frontal I Robot euro cut."
It is also possible that a Euro theatrical version with full frontal existed, but the DVD/BluRay releases used the US cut.