  We present results on the QCD equation of state, obtained with two different
improved dynamical staggered fermion actions and almost physical quark masses.
Lattice cut-off effects are discussed in detail as results for three different
lattice spacings are available now, i.e. results have been obtained on lattices
with temporal extent of $N_\tau=4,6$ and 8. Furthermore we discuss the Taylor
expansion approach to non-zero baryon chemical potential by means of an
expansion of the pressure. We use the expansion coefficients to calculate
various fluctuations and correlations among hadronic charges. We find that the
correlations reproduce the qualitative behavior of the resonance gas model
below $T_c$ and start to agree with the free gas predictions for $T\gsim
1.5T_c$.
