They are a little dated these days of course, but off the top of my head fingerprints are used for banking, old fashioned wire transfers, and passports. They want to be able to connect you to those things, and the fingerprint was the private key signature [1] of the 20th century.

Which, IMO, isn't "so 1984" because those are historically all major fraud avenues.

[1]: http://en.wikipedia.org/wiki/Digital_signature