Running mean, median and others

The running mean (moving average) can be calculated in R by means of the function
x <- c(1,2,4,2,3,4,2,3)
filter(x, rep(1/3,3) )

and the running median by
runmed(x,3)

sequential differences by
diff(x)

for other statistics use the library zoo (and there maybe rollapply).
The time series functions can also be useful for similar problems (e.g. deltat, cycle).

package {caTools} has implemented some fast algorithms for similar purposes:
runmean(x), rumin(x), runmax(x), runquantile(x), runmad(x), runsd(x)