>are there any other examples of this in nature?

It's pretty common, but doesn't always happen.

>do ligers have the same issue in terms of reproducing?

Ligers are generally fertile. Note that it's not a hard cutoff, there's a range between hybrids that are almost always fertile and those that are almost always infertile. Plenty of species fall in the middle ground.

>is this why a chimpanzee and a human couldn't reproduce?

This has never really been thoroughly investigated, so we don't actually know if hybrids are possible. Hybrid incompatibility is about more than just differences in chromosome number, though. Specific adaptations can make egg and sperm incompatible (related species with overlapping ranges sometimes have adaptations like this to prevent hybrids) and sometimes the details of genetics can make hybrids nonviable.