Very few cities have 24/7 subway service. NYC is pretty much the only one I can think of. German cities generally have 24 hour service on the weekends, but not through the week.
A few others: Chicago, Philadelphia, Copenhagen. I am a bit biased, but I think Copenhagen has the best service in that regard. Almost any main transit route runs 24/7: the metro, the 9 'A' trunk bus routes, most of the commuter-rail 'S-train' lines, and even the international 'Øresundståg' train service to Malmö. It makes a nice difference in peace of mind, because you never have to worry about being stranded anywhere.
Stockholm have comparable service level during nights as well. Although some smaller trains don't run for a few hours during the night, even on weekends.
Philadelphia has VERY little 24 hour service. Last I checked two bus routes operate along the same path as the 'orange' and 'blue' subway lines and nothing else. The regional rail service shuts down by midnight.