In celebration of nascent 2013, below are some photographs of Times Square (or Longacre Square as it was known before 1904), from New York Public Library and the New York Historical Society, two organizations with some lovely photographic collections. Note that in these early images one can actually see the Times building!
[Note that these are links due to copyright restrictions.]
New York Public Library:
From the New York Historical Society:
Other amazing digital collections can be found at the Metropolitan New York Library Council.