Some do, some don't. It's obviously less expensive to produce them without the core passages so there's a cost/performance tradeoff.
When they do, a ceramic core, the shape of the desired passages, are placed in the wax injector mold before the wax is injected. The wax then covers the ceramic core. A monoshell coating is applied by dipping in slurries and coating with sand-like material, building up the shell. When dried, the wax is melted out leaving cavities the shape of the desired part. The empty monoshell is pre-heated then the alloy is poured in to form the casting. After cooling, the monoshell is broken off and the ceramic core removed via a caustic bath.
Core passages are also used on vanes (which do not rotate like blades) primarily for weight reduction.