Starting from a (new physics independent) tree level determination of rhobar and etabar, we perform the Unitarity Triangle analysis in general extensions of the Standard Model with arbitrary new physics contributions to loop-mediated processes. Using a simple parameterization, we determine the allowed ranges of non-standard contributions to |Delta F|=2 processes. Remarkably, the recent measurements from B factories allow us to determine with good precision the shape of the Unitarity Triangle even in the presence of new physics, and to derive stringent constraints on non-standard contributions to |Delta F|=2 processes. Since the present experimental constraints favour models with Minimal Flavour Violation, we present the determination of the Universal Unitarity Triangle that can be defined in this class of extensions of the Standard Model. Finally, we perform a combined fit of the Unitarity Triangle and of new physics contributions in Minimal Flavour Violation, reaching a sensitivity to a new physics scale of about 5 TeV. We also extrapolate all these analyses into a "year 2010" scenario for experimental and theoretical inputs in the flavour sector. All the results presented in this paper are also available at the URL www.utfit.org, where they are continuously updated.