We present experimental studies of high-order harmonic generation in t
he rare gases performed with a short-pulse titanium sapphire laser ope
rating at 794 nm in the 10(14)-10(15) W/cm2 range. The harmonic yields
generated in neon and in argon are studied for all orders as a functi
on of the laser intensity. They vary first rather steeply, in the cuto
ff region, then much more slowly in the plateau region, and, finally,
they saturate when the medium gets ionized. The dependence of the high
-order harmonic cutoff with the laser intensity in neon and argon is f
ound to be lower than that predicted in single-atom theories. We obser
ve high-order harmonics in argon and xenon (up to the 65th and 45th, r
espectively) at 10(15) W/cm2, which we attribute to harmonic generatio
n from ions. We also show how the harmonic and fundamental spectra get
blueshifted when the medium becomes ionized.