(1) This is my credit score, certified by XYZ agency, so please don't ask for my SSN so that you can lose it in a public database leak tmrw
(2) Here's a bug in your program, please give me the bug bounty and I will tell you the bug (can help stop sketchy bug bounty programs.)
(3) Your Certificate Transparency Provider can prove that, for the latest root, there was no change in your certificate. (This has less to do with privacy and more to do with the succinct verification properties of the latest zkps)
(4) Construct postquantum-secure signatures (eg: the Picnic signature scheme)
Generally, ZKPs provide selective disclosure: I can prove to you that some fact about me or my accounts is true, without revealing to you any other information. The SSN example is one, you could generalize that to taxes, bank statements, Keybase attestations, etc.