I understand that the only two (2) species on the planet that have
unique fingerprints are humans and koalas'. Is this true?

Actually, all primates have unique fingerprints. Scientists
investigating animals such as chimps, orangutans, and gorillas
sometimes keep a record of each animal's fingerprints for
identification purposes.

Here you can see the fingerprints of several different primates:

Lisa Roet Gallery
http://www.lisaroet.com/gal6.html

"All gorillas have unique fingerprints like humans."

The Primates: Life in the Trees
http://www-personal.umich.edu/~phyl/anthro/lifetrees.html 

"Gorillas (indeed, ALL primates) have fingerprints."

Tremendous Trifles: Apes
http://members.fortunecity.com/husom/Trifles/Animals/Apes/Apes.html 

"Fingerprints are unique to each individual. Each human being is
completely unique. Other primates also have unique fingerprints e.g.
gorillas."

Kevin Callahan's Lab Notebook Fall 1997
http://www.geocities.com/Athens/Parthenon/7644/lab2.html

"Q: Do other primates, such as apes, chimps, and monkeys, also have
fingerprints? If so, are they also unique to that individual?

A: Yes to your first question and yes to the second, and, even more
surprising-some monkeys have fingerprints on their tails."

USA Today: WonderQuest
http://www.usatoday.com/weather/wonderquest/wquest100400.htm

"Not only do primates have fingerprints and toeprints, some even have
tailprints. A few of the New World monkeys (those found in Central and
South America) have prehensile tails, which means that they can use
their tails to grasp objects. Parts of their tails feature dermal
ridges, the fine lines you see when you look closely at your fingers.
According to an article from naturalSCIENCE, fingerprints, also known
as dermatoglyphes, are 'typical for higher primates, but occur
sporadically in other mammals.' Koala bears have fingerprints, with
dermal ridges on part of their palms, unlike the palms of humans and
primates, which are thoroughly covered with ridges. Scientists believe
fingerprints serve two purposes -- they allow us to grasp objects
better by providing added friction, and they increase the sense of
touch.

Just as in humans, the fingerprints of primates are unique."

Ask Yahoo: Do primates have fingerprints?
http://ask.yahoo.com/ask/20020315.html

There's an interesting article about koalas' fingerprints on this page:

NaturalSCIENCE: Fingerprint homoplasy: koalas and humans 
http://naturalscience.com/ns/articles/01-04/ns_hll.html

Google Web Search: "fingerprints" + "primates"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=fingerprints+primates

I hope this information is useful. If anything is unclear, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

It is often assumed, but has never really been proven, that
fingerprints are unique, in humarns or other animals.   The history of
this apparently involves an assertion (early in the 20th century, as I
recall) that they were unique, this assertion was accepted by a court,
and they've been pretty much never really been analyzed thoroughly
beyond that.

(It's not clear to me how you'd go about proving it anyway, since the
pattern of fingerprints for any individual is a function of his
environment during gestation (yes, identical twins do have different
fingerprints..).   So the best you could hope to do is to prove the
odds of an interference are vanishingly small.

Ty, You prove it the same way you prove no two snowflakes are alike -
by examining them all.