NYC: no duty to protect
Here's a classic case of it, arising in Mayor Bloomberg's own city. A violent lunatic begins stabbing people. Police are present, but flee and lock themselves in the conductor's car for protection. An unarmed witness wrestles the lunatic down, but is stabbed and cut in the process. Eventually, the NYPD officers emerge from their hiding place.
Held: the fellow who tackled the lunatic when the officers fled has no right to sue the city.