You can find the minimum crew required in the aircraft Type Certificate Data Sheet (TCDS). It is available from this FAA link (the FAA's Dynamic Regulatory System - DRS).
Note: In the search criteria field (in the DRS) when you enter the aircraft you're interested in, just use the model number. For example, for a Boeing 737 you would type in 737, not B737, for a Learjet 24 you would type in 24, etc.
Here is a TCDS example/excerpt from the FAA's Dynamic Regulatory System for the 737:
(emphasis is mine)
Also, there are certain types of operations where a single-pilot certificated aircraft requires two pilots. For example, under FAR Part 135, a Cessna 172 (type certificated requiring a single pilot), operating under IFR and not equipped with an approved autopilot (the use of which is authorized by operations specifications), requires a second-in-command when carrying passengers - (Source 1) and (Source 2).