The answer to that question depends on a couple of things:
Are the cabinets finished in a factory or finished in the home? Factory finish cabinets are modular boxes (looking inside each cabinet you will see them separated from each other by sidewalls) and have been installed more recently, in the last 15 years. For these cabinets, soap and water can be used, or for heavier grime and grease, a product called Cabinet Magic works great. Other products similar to this should available at a local hardware store near you. Just make sure, with a factory finished cabinets you do not use a silicon-based product, it will strip the finish.
Be careful cleaning a cabinet finished in the home, by the time the grease has build up it is mixed in with the top finish coat of the cabinet. To clean the cabinets is to take off this top coat. A properly “cleaned” cabinet at this point involves removing this top layer and reapplying a new top coat.
However, for a small confined area, such as around the handles, you can use a very dull razor blade to scrap off any built-up grime and then clean with a wet sponge and grease cutter, such as Dawn soap. If touch-ups to the finish are necessary, a top coat, such as polyurethane, can often do the trick. Consult with your local paint store about what product is best to use for your cabinets.
This article from our website has details on how to identify the difference between factory and finished-in-home cabinets: http://cabinets-q-and-a.com/exist-kitchen-cabinet.html