How many fraternities are there in the US?

Hundreds.

There are hundreds of fraternities in the United States. Greekrank.com lists 80 Greek college- and university-based fraternities in the US. The article Social Fraternities and Sororities – History, Characteristics of Fraternities and Sororities, Reforms and Renewal reports that in the year 2000 there are 66 national fraternities having more than 5,500 chapters with 370,000 members in the US and Canada.