Yes, "New York Times" should be italicized to indicate that it is the title of a newspaper.
The New York Times
The New York Times rule is a rule of conduct that a person should not be involved in any activity that they would not mind having published on the front page of the New York Times. This rule is also called the New York Times versus Sullivan rule.
No, "New York Times" does not have to be underlined on a book cover. Typically, it is either italicized or presented in a specific font style to denote it as a title. The specific formatting may depend on the publisher's style guide or the design preferences for the cover. Always check for any specific guidelines if you're working on a project that involves its use.
New York, New York.
The New York Times Company owns The New York Times, of whom the CEO is Mark Thompson.
Perhaps the New York Times is still around.
New York Times Building is a building found at New York City in USA.
The New York Times is also known as NYT or simply The Times.
The New york times
The population in New York in colonial times was diverse.
The New York Times Almanac was created in 1997.
The New York Times Crosswords happened in 2007.