In this paper we describe the features of the SMILETRAP Penning trap mass spectrometer and give examples of recently performed precision mass measurements. SMILETRAP is designed for precision mass measurements using the merits of highly-charged ions. We emphasize here the importance of accurate masses of hydrogen-like and lithium-like ions for the evaluation of g-factor measurements of electrons bound to even-even nuclei and test quantum electrodynamics (QED). For these experiments the ion masses of 40Ca17+ and 40Ca19+ were measured at SMILETRAP with 5 × 10-10 precision. Highly precise mass measurements can also be used for testing atomic structure calculations and determination of atomic and nuclear binding energies. Some Q-values are of fundamental interest, for example, the beta-decay of tritium and the double beta-decay with no neutrinos of several nuclei, in particular 76Ge. These decays are related to properties of the electron neutrino mass and whether this neutrino is a Majorana particle. The reason that Penning traps are so reliable for the determinations of accurate decay Q-values is due to the fact that systematic errors to a great deal cancel in the mass difference between the two atoms defining the Q-value. In this paper we report the most accurate Q-values of these two beta decays namely 18589.8(12) eV for the tritium decay, and 2038.997(46) keV for the neutrinoless double beta-decay of 76Ge.