667 = 23 x 29. It is the product of two successive primes (A006094) and two distinct Sophie Germain primes (A157344).
667 is the maximum number of regions into which 36 lines divide the plane (A000124).
667 is the number of asymmetric trees with 16 vertices (A000220).
667, 669, and 671 are all semiprimes (A092125).
667 YCF was on the license plates of the car driven by Meeno Paloma (Lou Diamond Philips) in the 2009 movie The Triangle.
Source: Prime Curios!