We report on replica-exchange simulations of the folding of a 21-residue alpha-helical peptide in explicit solvent. Using eight replicas over a 280-450 K temperature range, we were able to simulate both the folding equilibrium and the helix formation process. While the melting temperature was exaggerated by about 50 K, the folding enthalpy and entropy were in good agreement with experimental data. Simulations of the helix formation process showed a sequential mechanism, with helical structures formed within ca. 3 ns of simulation, and confirmed that the alpha-helical state was a global free energy minimum of the peptide at low temperatures. We also present long-term conventional MD simulations of several simple peptide model systems for which we compare simulation results to experimental data, in order to test current peptide and water models.