In an extensive CCD photometric survey of potential old open clusters, we have identified a number of systems that are indeed old; some of them are among the oldest of the open clusters. Using our versions of two well-known morphological age indices, one based on the luminosity difference between the main sequence turnoff and the horizontal branch and the other on the color difference between the turnoff and the giant branch, we have ranked the open clusters in approximate order of age. Our data together with previously published photometry of other old open clusters, yields a catalogue of 72 clusters of the age of Hyades or older with 19 of the clusters as old or older than M67 (about 5 Gyr). Among the oldest open clusters are Be 17, Cr 261, NGC 6791, Be 54, and AM 2. Be 17 and another old cluster, Lynga 7, are possibly as old as the youngest globulars. The data also suggest that the formation rate of open clusters may have been higher early in the history of the disk than at intermediate times since numerous clusters have survived from that time.