  The recent observation of the pulsar PSR J1614-2230 with a mass of 1.97 +/-
0.04 M_sun gives a strong constraint on the quark and nuclear matter equations
of state (EoS). We explore the parameter ranges for a parameterized EoS for
quark stars. We find that strange stars, made of absolutely stable strange
quark matter, comply with the new constraint only if effects from the strong
coupling constant and color-superconductivity are taken into account. Hybrid
stars, compact stars with a quark matter core and an hadronic outer layer, can
be as massive as 2 M_sun, but only for a significantly limited range of
parameters. We demonstrate that the appearance of quark matter in massive stars
depends crucially on the stiffness of the nuclear matter EoS. We show that the
masses of hybrid stars stay below the ones of hadronic and pure quark stars,
due to the softening of the EoS at the quark-hadron phase transition.
