How many nuclear weapons are there in the world?

Globally there are now  approximately 17,300 nuclear warheads.
(Upated as of early 2013)

Russia 8,500
United States 7,700
France 300
China 250
United Kingdom 225
Israel 80
Pakistan 100-120
India 90-110
North Korea <10

Estimated Total:  17,300

This total is from the Federation of American Scientists source:
http://www.fas.org/programs/ssp/nukes/nukestatus.html

(FAS data is from the Nuclear Notebook in the Bulletin of the Atomic Scientists,
and the nuclear appendix in the SIPRI Yearbook.)

This is a decrease from the global high of 70,000 nuclear warheads in 1986.

For updates or comparisons, go to:

The Bulletin of the Atomic Scientists
Center for Defense Information (Washington)
SIPRI

SIPRI Media Release of 16 June 2014:
"Nuclear Forces reduced, while modernization continues, says SIPRI"
http://www.sipri.org/media/pressreleases/2014/nuclear_May_2014

(Note that where there are discrepancies about numbers, you may wish to check the above sources and compare.)

To view the world Proliferation Status and Warheads (2007) map (a list of countries Possessing Ballistic Missiles, and how many) go to The Carnegie Endowment for International Peace site here 

For a graphic idea of the number of nuclear weapons currently in the US arsenal, have a look at the "ball bearing demonstration": http://truemajority.org/fun/