I have a credit card called Final VISA that does it as their main feature. (Signed up for it from here on HN; it's OK.)

Another company, Privacy.com, does on-the-fly numbers as debit cards drafting from your bank account.

Such a shame that Privacy.com app is country locked, I'm from South Africa and would definitely use something like this

Bank of America does. Only for credit cards though.

I know Discover offered it about ten years ago (saw a friend use it). I don't know if they still do. Always thought it was a cool feature and wanted a card that would allow it, but up to this point I don't think any of mine do.

Discover stopped offering them a few years back. At one time I had three cards that had this option and they all slowly stopped, basically saying their fraud detection was good enough the extra trouble wasn't worth it for them.

BoA appears to have it.

https://www.bankofamerica.com/privacy/accounts-cards/shopsaf...

Certain Citibank cards (not all though)

My bank in Sweden supports it for their MasterCard debit cards

My Citibank MasterCard provides one-time use CC number.