Thanks to both the German Genealogy Group and the Italian Genealogical Group, an index to New York City births 1901-1907 is now available online. The records were indexed by volunteers representing many different ethnic groups.
The index is a great convenience but, of course, it is only an index. Genealogists should first find the records of interest in the index, then consult the original records on microfilm to obtain all the details. Images of the original birth records are available on microfilm at the New York City Municipal Archives with copies available through the LDS Family History Library in Salt Lake City and Family History Centers around the world.
You should also realize that many births of these years were not reported simply because many took place at home and were never reported to authorities.
You can find the New York City Birth Records from 1901 through 1907 at both http://www.italiangen.org/NYCBirthsearch.asp and at http://www.germangenealogygroup.com/NYCBirthSearch.asp.
Volunteer efforts are great, but they do not operate without significant funding. If you'd like to support the Italian Genealogical Group in adding even more records in the future, go to http://www.italiangen.org/predblist.stm.
Steve Morse has also created a One-Step search tool for these records that is available at http://stevemorse.org/vital/nybirthigg.html. I tried a search from the One-Step search tool and found it to be super-simple to use. Enter whatever info you have: first name, last name (using "is exactly," "sounds like," starts with," "contains," or "ends with." you may also enter county, certificate number, year for beginning of search, year for end of search, birthday (month and date of the month). Any information you do not have can be left blank. The search will then return all the records that match the parameters you specified.
Great work, Steve!