I've been told that in New York City, no less than 20% tip is expected in a restaurant. I've always thought you could tip anywhere from 10-20% in a restaurant depending on service quality. Is 20% really the bottom of the tipping range in NYC restaurants?
For the US in general, 15% is the commonly expected bottom line, not 10, unless you're trying to send a mean spirited message to your server. 20% is far from unheard of.
In NYC in particular, 17% is probably the most common number - this is because NY Sales Tax on your restaurant bill is 8.5%, and most people just double the tax to calculate their tip - possibly adjusting upward to a multiple of 5, 10 or 20 to avoid dealing with change when paying cash.
For drinks at a bar, the custom is to tip 1-2 dollars a drink (depending on the price of the drink, I tend to a dollar per digit of the drink price).
Be advised that some restaurants will automatically include the tip in your bill. Generally listed as a 'Gratuity' or 'Service Charge'. This is particularly common if you're dining in a large group, but some unscrupulous or cynical restaurants will do this automatically for anyone who seems like they're from a country where tipping isn't customary. Regardless, if this is done, it will always be clearly stated on the bill, so you'll know you don't need to leave any additional tip above and beyond that. (Unless you'd like to do so to reward exceptionally good service!)
Also note that tipping is not expected at fast food or similar places, such as a McDonalds, Deli, Starbucks or a Pizzeria. While many such places will have a 'tip jar' on the counter next to the register, tossing some change in is purely optional and not expected.