I have to respectfully disagree. Yes, oil is great in closed systems with tight tolerances, crank shafts, and transmission gear meshes. Grease is better left to closed systems or in applications where the grease exposed to dirt will not be able to work its way back onto the wear surfaces. Think of pins that hold hydraulic cylinders at pivot points or driveshaft joints. I would absolutely never put grease on an exposed chain or roller, as a dry lube or chain oil will be much better.

Edit: If it has a grease zerk, then grease it. For most other things, there is probably something better