The job of the fuel processor is to provide relatively pure hydrogen to a fuel cell, using a fuel that is readily available or easily transportable. Fuel processors must be able to do this in an efficient manner with a minimum of pollution -- otherwise, they negate the benefits of using a fuel cell in the first place.
For cars, the main issue is energy storage. In order to avoid having large, heavy pressure tanks, a liquid fuel is preferable to a gas. Companies are working on fuel processors for liquid fuels like gasoline and methanol. Methanol is the most promising fuel in the short term; it can be stored and distributed in much the same way as gasoline is now.
For houses and stationary power generation, fuels like natural gas or propane are preferred. Many power stations and houses are already hooked up to natural gas supplies by pipeline. And some houses that are not hooked up to gas lines have propane tanks. So it makes sense to convert these fuels to hydrogen for use in stationary fuel cells.
Both methanol and natural gas can be converted to hydrogen in a steam reformer.