Peptides often have conformational preferences. We simulated 133 peptide 8-mer fragments from six different proteins, sampled by replica-exchange molecular dynamics using Amber7 with a GB/SA (generalized-Born/solvent-accessible electrostatic approximation to water) implicit solvent. We found that 85 of the peptides have no preferred structure, while 48 of them converge to a preferred structure. In 85% of the converged cases (41 peptides), the structures found by the simulations bear some resemblance to their native structures, based on a coarse-grained backbone description. In particular, all seven of the beta hairpins in the native structures contain a fragment in the turn that is highly structured. In the eight cases where the bioinformatics-based I-sites library picks out native-like structures, the present simulations are largely in agreement. Such physics-based modeling may be useful for identifying early nuclei in folding kinetics and for assisting in protein-structure prediction methods that utilize the assembly of peptide fragments.