Some of my expat friends and I have pets here in Germany. I personally have quickly learned that what one does with one's animal in the first country might not be common, or even allowed, in the next.
Take, for example, declawing cats. It is allowed (but sometimes controversial) in the US but is definitely not allowed in Germany. Imagine the weird looks when I told potential landlords during my apartment search that Moo was declawed. I kept getting these strange looks and thought that maybe it was a language barrier and I wasn't explaining it correctly. In the US, some apartments only allow declawed cats. I received Moo as an adult cat in the US and he had already been declawed. Once I realized that declawing was illegal in Germany, I stopped telling them that my cat had been (legally) "mutilated" in the US. Instead, I told them that he is a good cat and he doesn't ruin things. I figured that would cover all the basis, and it's true. I mean, once in a while, he does run around the apartment and bunches up a throw rug as a result, but that's easily fixed.
Here's another cultural difference: my friend was told that Germans don't clip their cats' toenails (usually). By clipping, I mean just using cat nail clippers to remove the extra tips of the nails that might grow too long into the cat's pads on its feet. I was curious if this is true, so I asked a German colleague. She said that she doesn't trim her cat's toenails, either, and she doesn't know anyone else who does. She has a scratching post and that keeps their nails short enough.
This was very interesting to me. In the US, it seems pretty common to use nail clippers on a cat, even with a scratching post. One of my friends has to do this because the cat's dewclaws, when grown too long, start to curl into the pads of the cat's feet. This is even a cat who uses the scratching post regularly.
In my own experience, I am a "bad" cat owner by US standards, but a "normal" cat owner by German standards. Moo was declawed on his front paws so he does still have back claws. I used to trim them but noticed that he would chew on them himself. I stopped trimming his toenails as a test and have not trimmed them since. He hasn't had any problems. I would imagine it depends on the cat; a friend in the US definitely has to trim her cat's toenails or the poor cat is uncomfortable because of the way they grow.
I asked about trimming dogs' toenails, and my colleague said that people do trim those.