A systematic search of the IRAS point-source catalog has identified eight new nearby stars which are "Vega-like" in terms of their large 60-micron excess. This brings to twelve, of the set of 36 nearby dwarfs and subgiants which are bright enough to have IRAS catalog fluxes at 12, 25, and 60 microns, the total number of known Vega-like stars within 25 parsecs of the sun. Two significant effects distinguish these twelve stars from the 24 stars without 60-micron excess: The predominance of spectral type A and the absence of double stars in the Vega-like group. While both effects are intuitively consistent with the interpretation that the 60-micron excess radiation is due to a disk of protoplanetary material, suggesting an early phase in the evolution of a planetary system, this distribution can also be due to luminosity and brightness selection effects. A large fraction of the F, G, and K main-sequence stars, i.e., stars with longer main-sequence lifetimes than A stars, may thus also be surrounded by disks, but only the warmest of these disks are identifiable with high confidence in the IRAS catalog by their 60-micron excesses.