Results from an extensive database analysis of JET density profiles in stationary conditions show that the density peaking factor n(e0)/< n(e)> in JET H modes increases from near 1.2 at high collisionality to around 1.5 as the plasma collisionality decreases towards the values expected for ITER. This result confirms an earlier observation on AUG. The density peaking behaviour of L modes is remarkably different from that of H modes, scaling with overall plasma shear as (n(e0)/< n(e)> similar to 1.5l(i)), independently of collisionality. H-mode density profiles show no shear dependence, except at the lowest collisionalities. No evidence for L-Te, L-Ti, rho* or beta dependences has been obtained. Carbon impurity density profiles from charge exchange spectroscopy are always less peaked than electron density profiles and usually flat in H modes. The peaking of the electron density profiles, together with the flatness of the impurity density profiles, are favourable for fusion performance if they can be extrapolated to ignited conditions.