The dialing rule in New York City for landline-originated calls is currently (January 2008):
Calls within your own area code may be dialed as 10D or 1+10D Calls outside your area code must be dialed as 1+10D. Yes, even if that other area code is overlaid with your own.
The rule when making a cell-originated call from NYC is:
All calls are 10D regardless of area code, state or country.
Yes, I have called the Dominican Republic, area code 809 at the time, from a cell phone, with just 10 digits.
In other words, yes, when calling outbound from NYC on a landline or cell phone, the 1+ is meanlingless. 1+ could be removed from all calls and the dialing plan would work just fine.
In some rare cases, if you happen to be roaming in another cell company's territory, and they give you a recording that you must dial1 first, then hang up and do so. (In recent years, I've only had that happen when roaming in two places: Ottawa, Ontario and Basseterre, St Kitts and Nevis.)
In an even more rare case, when roaming in Antigua, I also had to dial1+ when calling from my NYC-based cell phone back to the US. If I dialed 212-nxx-xxxx instead of 1-212-nxx-xxxx, I got routed to (get this) Morrocco, which is country code +212. In other words, the Antiguan cell carrier assumed that all cell roamers were, by definition, making international calls and therefore the first digit was assumed to be the start of the country code. They didn't require 011+. This was in 2003, when using an old AT&T Wireless TDMA phone, and may no longer apply.
Greg Monti New York, NY