cats

I've always had a lot of success with holding out my hand towards the cat, palm down, limp, and allowing the cat to inspect it in their own time.

I've heard this is also a technique from experts, but I just found it when we had a cat. It seems to work on dogs too.

It's non-threatening, and it doesn't put any pressure on them for a response. Just get it close enough to be just outside their personal space. If they stretch their nose towards it to sniff, you can bring it closer, and then you may just get the coveted nose bump and cheek nuzzle.

You may also get the, "what are you doing, you freak, leave me alone" body language, in which case you just have to wait and try again later.