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The wikipedia article on human height reports mean height for many different countries by sex but it does not report standard deviations.
What is the standard deviation of adult human heights within sexes?
Obviously the size of the standard deviation would vary across countries and by other factors. That said, I think good data on a few representative countries would be sufficient to get a reasonable sense of what it typically is and the extent to which the standard deviation varies.
It's probably around 7 cm for men and 6 cm for women.
The Evolution of Adult Height in Europe, which is a source for some of the statistics reported on that Wikipedia page, gives averages, standard deviations, and sample sizes for both sexes across 10 european countries (and across a number of different age cohorts).
Taking their numbers for men and women born between 1966 and 1978, the average male standard deviation of height across all ten countries is 7 cm (range 6.7-7.3) and female 6.1 (range 5.6-6.4).
For a more global context, Subramanian et al. give heights with standard deviations for a much wider selection of countries, mostly "developing countries". Unfortunately for your question, they only report numbers for women. However, these look pretty similar to the Europe numbers: the across-country average SD for women is 6.3. (with all these countries, the range is greater at 5.4-8.1, but 32 out of the 54 countries have SDs within the Europe range for women, i.e. 5.6-6.4)
Note: for this estimate I just ran averages across years/countries, I didn't weight the averages by sample size.
