There are many iPhone apps available to help a visitor around New York and a few for the Android phones too.  Please share your favourites here.

Here's a short listing of iPhone/iPod Touch apps  and e-books you may find to be helpful when in NYC

iPhone/iPad 

BeSafe! 

An app for a safe travel that lets you assess your safety or danger level based on your location in NYC, London and Paris, and on the time of the day. Maps of the 80 precincts are available, as well as hotspots of the most dangerous subway stations, places where pickpockets and prowl, and where crimes are most often committed. Really useful when you don't know the city.
http://itunes.apple.com/us/app/besafe...

 

Embark NYC

Embark NYC makes taking the subway simple and elegant. It provides everything necessary to get around on the New York subway, and it even works underground! 

 

Hopstop

This app, which was launched for use in NYC, gives you door-to-door transit, walking, biking and taxi directions in over 300 cities worldwide. This app is great for those who are traveling to outer boroughs (Brooklyn, Bronx, Queens and Staten Island), as well as Long Island, North of NYC (Westchester and Connecticut) and New Jersey because it includes railroad routes (LIRR - Long Island Rail Road; Metro North and New Jersey Transit) in the directions it gives you. It also includes bus routes, which is a necessity in neighborhoods where the subways/trains don't reach - many of these exist in the outer boroughs. https://www.hopstop.com/mobile

 

Twitter

If not for anything else, make sure to have the Twitter app handy to follow MTA's service alert updates: @NYCTSubway and @NYCTBus. These give up to the minute alerts on any changes or delays on trains/buses and allows you to plan accordingly. You can select to have these alerts text to you, but it can become a little bothersome since they tweet so frequently and many of the tweets won't pertain to your specific travel needs/plans. This is especially helpful in inclement weather when you know there will be issues.

For iPhone/iPad: https://itunes.apple.com/us/app/twitt...

For Android: https://play.google.com/store/apps/de...

 

MoMA 

For most people, modern art is something that goes down a little easier with some explanation. Instead of standing in front of a painting thinking, “I just don’t get it,” the MoMA app helps by pulling up an audio tutorial talking about the painting or special exhibit. You’ll like it so much that you’ll want to come back for all new exhibits and special events (which are also conveniently updated regularly in the app). 

MTA: Information source about New York Travel Phone Apps from the MTA dot info   

TKTS

Issued by the not-for-profit that operates the TKTS "half-price" booths in three locations, it allows you to see the list of shows posted at those booths, in real time. It does not provide any sort of ticket purchasing. You still have to walk to one of the booths, but you can learn what's posted before you go. Naturally, tickets may be depleted for some shows by the time you get to the window.

https://itunes.apple.com/us/app/tkts/...
https://play.google.com/store/apps/de... 

Here is a link to Inside United States: Travel Apps in USA ~ It contains some information about Travel Apps for New York City.  

Station App

Station is an iPhone app that helps users quickly and easily find places and things around public transportation stops/stations.  Whether you are searching for a restaurant, park or something else, Station makes it pretty easy.  Type in what you’re looking for, type in a public transit stop and find exactly what’s within walking distance.  Station is Free.  www.stationapp.eu