Singapore, for one. But then again they fingerprint and take photos at manual counters too. They started to "offer" (read: force) citizens of a lot of countries the use of automated immigration gates in 2023, and when I had to use them late 2023, they didn't work so well. 5 attempts each on entry and exit, all failed. ICA officers were displeased, but what can I do...
Hong Kong. Residents need to give their thumbs' thumbprints for their HKID, used at the eChannel. Visitors who are eligible to register for the eChannel for frequent visitors give their index fingers' thumbprints. Enrolment is voluntary.
Permanent residents of HK and Macao can enter the other SAR with their ID card, after registering their ID card with the other SAR, passing along their photo and fingerprints. Again, that's voluntary. And they can apply for Mainland China's eGates too.
There's a trusted travelers system in Japan, voluntary and not so easy to get, that requires fingerprints too.