The regulations have been modified a couple of times in the past few years. Generally, individual photographers working with a tripod don't need a permit in the city now, as long as they don't have a crew of 5 people, and aren't using equipment like lighting that involves stretching cables on the sidewalk.

There are places where other regulations apply, like Grand Central Terminal (ask the Station Master for a tripod permit to shoot at times other than rush hour), or Battery Park and other nearby parks (permit required for commercial photography), or outside the New York Stock Exchange building (lots of security there), and you should avoid blocking busy sidewalks or creating a hazard, but otherwise it's not a problem. If you're not shooting in a busy pedestrian area, you're very unlikely to have any problems.