Most photographers have at least asked themselves this question. Some, like me, love processing. I am glad I have Photoshop, Lightroom, On1, Topaz, and Nik available to give my photos an artistic touch, or just to make them the best they can be. Other photographers want their photos to be finished straight out of the camera.
Cameras capture RAW data. What happens when you shoot in JPG mode? The camera does the processing for you! To give you a JPG, the camera decides how to interpret the data. On some cameras there are settings that will change how the data is interpreted, but it is still being processed.
I shoot in RAW. My goal is to have photos that are technically the best they can be out of the camera (which does not always happen--see my earlier blog post, Processing Can Be Fun). It's always easier to process when you have good basics, but if you shoot in RAW you usually need some processing.
Each person must figure out what works best for them. Learn all you can. Experiment, whether it is with your camera or on your computer. Let your photography express you, and only you can decide what that means.
To process or not to process -- what is your answer?