In the two parts of this contribution we describe two related XMM-Newton programs. The first part summarizes our study of the X-ray spectral properties and variability of z>4 quasars (Shemmer et al. 2005). The second part presents preliminary results from our ongoing XMM-Newton program to investigate the X-ray spectral properties and variability of luminous, high accretion-rate quasars at z~2--3. We find that the X-ray photon index does not depend on luminosity or redshift, and there is suggestive evidence that it may depend on the accretion rate. None of our quasars is significantly absorbed, and none shows signatures of reflection. By jointly fitting high-quality spectra of eight radio-quiet z>4 quasars, including three from our XMM-Newton observations, we place tight constraints on the mean X-ray spectral properties of such sources. Most of our quasars are significantly X-ray variable on timescales of months--years, but none shows rapid (~1 hr timescale) variations.