We present measurements of the quasar two-point correlation function, xi_{Q}, over the redshift range z=0.3-2.2 based upon data from the SDSS. Using a homogeneous sample of 30,239 quasars with spectroscopic redshifts from the DR5 Quasar Catalogue, our study represents the largest sample used for this type of investigation to date. With this redshift range and an areal coverage of approx 4,000 deg^2, we sample over 25 h^-3 Gpc^3 (comoving) assuming the current LCDM cosmology. Over this redshift range, we find that the redshift-space correlation function, xi(s), is adequately fit by a single power-law, with s_{0}=5.95+/-0.45 h^-1 Mpc and gamma_{s}=1.16+0.11-0.16 when fit over s=1-25 h^-1 Mpc. Using the projected correlation function we calculate the real-space correlation length, r_{0}=5.45+0.35-0.45 h^-1 Mpc and gamma=1.90+0.04-0.03, over scales of rp=1-130 h^-1 Mpc. Dividing the sample into redshift slices, we find very little, if any, evidence for the evolution of quasar clustering, with the redshift-space correlation length staying roughly constant at s_{0} ~ 6-7 h^-1 Mpc at z<2.2 (and only increasing at redshifts greater than this). Comparing our clustering measurements to those reported for X-ray selected AGN at z=0.5-1, we find reasonable agreement in some cases but significantly lower correlation lengths in others. We find that the linear bias evolves from b~1.4 at z=0.5 to b~3 at z=2.2, with b(z=1.27)=2.06+/-0.03 for the full sample. We compare our data to analytical models and infer that quasars inhabit dark matter haloes of constant mass M ~2 x 10^12 h^-1 M_Sol from redshifts z~2.5 (the peak of quasar activity) to z~0. [ABRIDGED]
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