Golf balls having a multi-layered core made of a foamed composition are provided. The core preferably has a foam inner core (center) and surrounding thermoset or thermoplastic outer core layer. Preferably, a polyurethane foam composition is used to form the foam center. The foam inner core preferably includes a fully-foamed center region and a partially or completely-collapsed foam outer region. The hardness of the fully-foamed region is different than the hardness of the collapsed foam region. Non-foamed thermoset or thermoplastic materials such as polybutadiene rubbers or ethylene acid copolymer ionomer may be used to form the outer core layer. The ball further includes a cover that may be multi-layered. The foam cores have good resiliency.