In Mike Lynch's "The Origins of Genome Architecture", he claims 10^13. I forget the primary source he cited, and since the book is in my office I can't check it now.
** Found the snippet that contained the reference. I think it's really worth including in its entirety.
A crude estimate of the amount of DNA within currently living
organisms can be made by noting that the length spanned by one base of
DNA is ~0.3x10^-12 km (Cook 2001).
The number of viral particles in the open oceans is ~10^30 (Suttle
2005). Assuming that there are twice as many viruses on land and in
fresh water does not change the global estimate very much at the
order-of-magnitude level. Thus, assuming an average viral genome size
of 10^4 bp, the total length of viral DNA if all chromosomes were
linearized and placed end to end is ~10^22 km.
The estimated global number of prokaryotic cells is ~10^30 (Whitman et
al. 1998), and assuming an average prokaryotic genome size of 3x10^6
bp yields an estimated total DNA length of 10^24 km.
With a total population size of 6x10^9 individuals, 10^13 cells per
individual (Baserga 1985), and a diploid genome size of 6x10^9 bp, the
amount of DNA occupied by the human population is ~10^20 km. Assuming
there are ~10^7 species of eukaryotes on Earth (~6 times the number
that have actually been identified), that the average eukaryotic
genome size is ~1% of humans, and that all species occupy
approximately the same amount of total biomass, total eukaryotic DNA
is ~10^5 times that for humans, or ~10^25 km.
Given the very approximate nature of these calculations, any one of
these estimates could be off by one or two orders of magnitude, but it
is difficult to escape the conclusion that the total amount of DNA in
living organisms is on the order of 10^25 km, which is equivalent to a
distance of 10^12 light years, or 10 times the diameter of the known
universe.
