  We present results and prospects for searches for rare B and D meson decays
with final state dimuons, including B_s\to\mu\mu, B_d\to\mu\mu, and D\to\mu\mu.
Upper limits on the branching fractions are compared to previous CDF
measurements, recent results from the B factories and theoretical expectations.
We also report on new measurements of production and decay properties of the
X(3872) particle, discovered in 2003 by the Belle Collaboration. New results on
the measurement of the relative branching fraction for the Cabibbo suppressed
decay B^+\to J/\psi\pi^+ Br(B^+\to J/\psi\pi^+)/Br(B^+\to J/\psi K^+) are
presented too. The presented results are based on the analyses of 70 to 220
pb^-1 of data collected by the CDF II detector in p\bar p collisions at
\sqrt{s} = 1.96 GeV at Fermilab Tevatron.
