Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally suitable for design. Rather, certain structures are distinguished by unusually high designability: the number of amino acid sequences for which they represent the unique lowest energy state; sequences associated with such structures possess both robustness to mutation and thermodynamic stability. Here we report that highly designable backbone conformations also emerge in a realistic off-lattice model. The highly designable conformations of a chain of 23 amino acids are identified and found to be remarkably insensitive to model parameters. Although some of these conformations correspond closely to known natural protein folds, such as the zinc finger and the helix-turn-helix motifs, others do not resemble known folds and may be candidates for novel fold design.