Not in the US, no. I ended up sending them my life story to convince them I was who I said I was, but they did not ask for fingerprints. I've never had to be fingerprinted for any reason. There is a palm geometry scan on file for me with a datacenter, but that works on a different principle.

If you're part of the Global Entry program, they have all 10 prints as well.

I think more countries' immigration controls require it for guest entry than departments of state require it for gaining a passport.