There are several issues that are common in whirlpool water heaters and several units have been recalled for safety and reliability issues.
Most common Fix for a Whirlpool Water Heater no pilot
Clogged Air Intake Screen
If you have an issue with your Whirlpool water heater pilot not lighting up, keep you fingers crossed and hope that this is the problem. As shown in the picture below the air intake on this water heater is on the bottom of the unit. If the unit has not been installed on bricks you may have some difficulty cleaning the filter. If this is the case try using the brush side on an ice scraper for your car. If you can try to fit a shop vac nozzle underneath the unit and clean it out.
Whirlpool Gas Water Heater Recalls
2005 Gas Water Heater – R110 Gas Valve
Number of Units – 178,000
The R110 Gas Control Valves are being recalled are installed on natural gas and liquid propane (LP) gas water heaters. The recalled valves were manufactured between July 25, 2005 and August 14, 2005 with production date codes 5-31 through and including 5-33, although not all valves with these date codes are affected.
2000-2006 Flame lock water heaters
All Whirlpool gas water heaters produced between 2000-2006 had a flame lock safety feature that has caused frequent problems for many owners. While there is no official recall for these water heaters they was some obvious fault recognized by Whirlpool who had a repair kit they sent out with no charge. The repair kit includes everything in the picture below. They will only send out the repair kit if the water heater is under warranty, otherwise the repair kit is $179 plus shipping. In this case you are much better off just replacing the water heater as often this only fixes the problem temporarily.