In 2007, a Swiss woman was unable to enter the USA as she had no fingerprints. She had a rare genetic disorder called adermatoglyphia.
CDNET,COM
When a print is taken, “instead of having a nice, regular pattern of concentric circles, you see a smear,” says study researcher Eli Sprecher at the Tel Aviv Sourasky Medical Center in Israel.

And now they've discovered the mutation behind the disease. The news could help us understand how fingerprints are made

So far, only 4 families have been documented for the condition. This includes a Swiss woman in her 20s trying to cross the US border in 2007. ScienceNow explains:

Peter Itin, a dermatologist at the University Hospital Basel in Switzerland, has dubbed it the "immigration delay disease" because sufferers have such a hard time entering foreign countries. In addition to smooth fingertips, they also produce less hand sweat than the average person.

(I probably would have made a Men in Black reference myself.) Turns out, 9 other members of the woman’s extended family were also smooth and ridgeless, which led researchers to suspect that the cause might be genetic.

Itin, Sprecher and colleagues collected DNA from the family and compared the genomes of family members with ADG to those of family members who have fingerprints:

They found differences in regions that were close to the genes and sequenced those.
One very short sequence overlapped with part of a gene called SMARCAD1, which was only expressed in the skin.

That gene was mutated in the fingerprintless family members but not in other members. In particular, the mutation isn't in a region of the gene that codes for the SMARCAD1 protein. Actually, the mutation causes copies of the SMARCAD1 gene to be unstable – it’s the first link in a long chain of events affecting fingerprint development before a person is born.