In this study, we address the questions of how important is the kinetics in protein aggregation, and what are the intrinsic properties of proteins that cause this behavior. On the basis of our recent quantitative calculation of the equilibrium phase diagram of natively folded alpha-helical and beta-sheet forming peptides, we perform molecular dynamics simulations to demonstrate how the aggregation mechanism and end product depend on the temperature, concentration, and starting point in the phase diagram. The results obtained show that there are severe differences between the thermodynamically predicted and the kinetically obtained aggregate structures. The observed differences help to rationalize the suggestion that monomeric proteins in their native functional structure can be metastable with respect to the amyloid state, and that the native fold is a special property that protects them from aggregation.