Here is a link to a pretty thorough about.com article: Will urine relieve the pain of a jellyfish sting?:
The article suggests that while urine may work in some circumstances, it can also cause the nematocysts in the wound to inject venom, which will actually make the pain worse.
Which brings us to urine. Urine
consists of water and waste products
of the body's blood stream, which
includes ammonia -- the reason for its
legendary use. Depending on the person
-- and whether he or she is dehydrated, diabetic, on a protein
diet, or dealing with myriad other
conditions -- urine may or may not be
about as good as fresh water. In fact,
urine contains so much fresh water
that stranded folks can drink their
own urine to survive (don't worry, I'm
cringing at the idea, too). Since we
know fresh water will often make
nematocysts fire, the logical
conclusion is that urine will do the
same thing.
Urine has about a 50/50 track record
on the Internet. Many anonymous
bloggers sing the praises of this
readily available wonder tonic, but
research just hasn't supported the
claims. Others tell stories of urine
not working at all. I've yet to read
any supposed first-hand claims that
urine made the pain of a jellyfish
sting worse.
It seems that acid can neutralize the venom that is released by the nematocysts, but urine does not always have the required acidity to get the job done.
Additional References (from the linked article):
Beadnell, C.E., et al."Management of a major box jellyfish (Chironex fleckeri) sting. Lessons from the first minutes and hours." Medical Journal of Australia. 4 May 1992 PMID: 1352619
Buddin, Elizabeth. "Jellyfish." Unk publish date. Sea Science. South Carolina Department of Natural Resources. Retrieved 23 Oct 2007
Fenner, P.J., et al."First aid treatment of jellyfish stings in Australia. Response to a newly differentiated species." Medical Journal of Australia. 5 Apr 1995 PMID: 8469205
O'Reilly, G.M., et al."Prospective study of jellyfish stings from tropical Australia, including the major box jellyfish Chironex fleckeri." Medical Journal of Australia. 3 Dec 2001 PMID: 11837877