Note that different formulas for computing skewness and kurtosis can be used. See, for example, the options "type" of the function kurtosis() shown by using ?kurtosis() after loading the package e1071 by using library(e1071).
I see that Jully Ouma has already mentioned the moments package. This is nice because it outputs a single figure. For a range of diagnostic and summary statistics, you could use describe() from the psych package, or if you want more detail you could try stat.desc() from the pastecs package. This is the most comprehensive of the options I think.
NOTE_PLS:- the syntax "Method" is a character string which specifies the method of computation. These are either "moment" or "fisher". {however, kurtosis allows in addition for "excess". i.e., If "excess" is selected, then the value of the kurtosis is computed by the "moment" method and a value of 3 will be subtracted.}
a) The "moment" method is based on the definitions of skewness and kurtosis for distributions; these forms should be used when resampling (bootstrap or jackknife).
b) The "fisher" method correspond to the usual "unbiased" definition of sample variance, although in the case of skewness and kurtosis exact unbiasedness is not possible.
**Aliter: other packages exist, of which one are "moments", "propagate" and "psych".