There have been a number of reports from photographers and tourists about NYPD forbidding them to take photos of such things as The Empire State Building, The Times Square Police Station, and photos on the New York City Subway. This is an NYPD OPS Order On Photography that was re-issued 4/03/09 (click to enlarge).
It is clear from the OPS Order above that NYPD is NOT allowed to view the photos taken without consent or direct you to delete them.
If traveling in New York City, I highly suggest printing a copy of this document out in case you run into an overzealous rookie.
[...] few months back I posted the NYPD OPS Order On Photography. If you read the OPS Order it is very specific that the laws and practices the NYPD abides by [...]