The Anatomy and Physics I class at Delaware Technical and Community
College has asked me to ask this question of Google's ace researchers:
One would expect that if you soak in a tub full of hot water, your
skin and the tissue immediately below it would expand (at least a
little). Why, then, do fingers shrink and wrinkle?

This exact question was discussed in a human physiology class that I
took in the 1960s. Basically, the answer is that only the outer
surfaces of our fingers and toes absorb water by osmosis, and expand,
while the layers beneath are waterproof. This results in the outer
skin being temporarily more ample than its underpinnings. It's as if
you are wearing a pair of socks that are much too large for you:
wrinkles result from the lack of tautness. Once the temporary
waterlogging has ended, and the top layer of skin returns to its
normal contours, the wrinkles disappear.

"The top layer of the skin is composed of toughened, scaly cells
collectively known as the stratum corneum. On most of the body, this
layer is quite thin, just .015 of a millimeter, but it's 40 times as
thick, or 0.6 of a millimeter, on the soles and palms.

Normally the stratum corneum is relatively dehydrated, but it absorbs
moisture and swells up when soaking. This swelling occurs throughout
the soles and palms, but it's most noticeable in the fingers and toes
because of their restricted dimensions... Since the underlying tissue
doesn't absorb water, the stratum corneum can't spread out and it
buckles like asphalt on the highway in the summer sun."

The Straight Dope Archives
http://www.straightdope.com/classics/a2_317a.html

Here you'll find some more explanations of this phenomenon:

Scientific American: Ask the Expert
http://www.sciam.com/askexpert_question.cfm?articleID=00027EB9-642A-1C72-9EB7809EC588F2D7

Ask Discover
http://www.discover.com/ask/main74.html

Department of Biology, Clemson University
http://biowww.clemson.edu/biolab/wrinkle.html

MSN: You Asked for It
http://encarta.msn.com/encnet/features/columns/?article=userquestions2#Why%20do%20our%20fingers%20wrinkle%20after%20we're%20in%20the%20water%20for%20a%20while?

Kids' Health
http://kidshealth.org/kid/talk/qa/wrinkly_fingers.html

ABC Online
http://www.abc.net.au/science/k2/homework/s95618.htm

This is the combination of search terms that brought me the best
results:

Google Web search: bath water wrinkle fingers
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=bath+water+wrinkle+fingers

If anything's unclear, please request clarification. I'm always
willing to re-ponder an interesting question like this one.

Best wishes,
pinkfreud

Fantastic work. The class can now pass.

Many thanks for the kind words, the five stars and the nice tip!

~Pink