We search for high-mass resonances decaying into Z boson pairs using data corresponding to 6 fb^-1 collected by the CDF experiment in pbar{p} collisions at sqrt{s}=1.96 TeV. The search is performed in three distinct final states: ZZ --> l^+l^-l^+l^-, ZZ --> l^+l^- u u, and ZZ --> l^+l^-jj. For a Randall-Sundrum graviton G*, the 95% CL upper limits on the production cross section times branching ratio to ZZ, sigma(pbar{p} --> G^* --> ZZ), vary between 0.26 pb and 0.045 pb in the mass range 300 < M_{G*} < 1000 GeV/c^2.