When would it be preferable to distinguish between capital and lowercase letters?

Wiktionary does it religiously, and it always makes the entries worse. Want to know what something means in German? Well, that's on a separate page.

Do you want to look something up while using your phone? Don't be stupid; use a desktop that won't autocapitalize the first letter you type in.

If you mean more from a user perspective, it really depends. For registry keys for example, since they're interacted with programmatically for the most part, I was expecting them to be case-sensitive. They're case-insensitive though, so that was a bit of a whiplash.