We discuss the phase diagram and the equation of state for QCD at non-zero temperature and density. We present results of a simulation for QCD with 2 flavors of p4-improved staggered fermion. Derivatives of the thermodynamic grand potential with respect to quark chemical potential $\mu_q$ up to fourth order are calculated, enabling estimates of the pressure, quark number density and associated susceptibilities as functions of $\mu_q$ via a Taylor series expansion. We also discuss the radius of convergence of the expansion as a function of temperature. It is found that the fluctuations in the quark number density increase in the vicinity of the phase transition temperature and the susceptibilities start to develop a pronounced peak as $\mu_q$ is increased. This suggests the presence of a critical endpoint in the $(\mu_q, T)$ plane.