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