We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at zlesssim 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at z = 0 for virial masses in the range 1011 h-1 M☉ <= M<= 1015 h-1 M☉ to lesssim5%, improving on previous results by a factor of 2-3. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at z = 0 and earlier epochs. Earlier studies have sought to calibrate a universal mass function, in the sense that the same functional form and parameters can be used for different cosmologies and redshifts when expressed in appropriate variables. In addition to our fitting formulae, our main finding is that the mass function cannot be represented by a universal function at this level or accuracy. The amplitude of the "universal" function decreases monotonically by ≈20%-50%, depending on the mass definition, from z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.