In 2002, scuba diver Tim Yarrow set a record for the longest time spent underwater after spending 10 days submerged in a tank in Johannesburg shopping center. When he finally emerged, his hands were spectacularly wrinkled.
The especially numerous dead keratin cells on our hands and feet absorb water when we're in the bath or going for a swim, but remain attached to our living cells, causing the appearance of wrinkles. Yarrow's hands show how extreme that absorption can get.
Edit: Commenter Aloicious points to this Nature article, which notes that the "pruney fingers" effect doesn't happen in people who have nerve damaged fingers, suggesting its the result of an autonomic nervous system rather than a result of absorption. Thank you, Aloicious!
Commenter Stephan Zielinski adds another Nature article, this one from a 1973 study, "The effects of prolonged water exposure on the human skin," which examined the effects of 72-144 hours of skin immersion in warm water. Although the wrinkling from brief immersion is a nervous system effect, after many, many hours, researchers in this study did find pronounced hydration and softening of tissue in the outermost layer of skin. This may be what we're seeing with Yarrow; it's simply unrelated to what we see in the bathtub.
The above is a screen grab from a recent segment of Outrageous Acts Of Science, which explains a bit more about Yarrow's ten days in the tank and warns that too much time underwater could lead to hazardous cracking of the skin:
[via Oddity Central]