After performing a practice instrument approach, the pilot performed a touch-and-go landing and remained in the airport traffic pattern for another landing. The pilot reported that the traffic pattern was busy, and that he was focused on a much slower airplane flying ahead of him. The pilot stated that he would normally put the landing gear down on downwind, but due to the distraction of the other traffic, he forgot to extend the landing gear. During the landing, the airplane skidded down the runway with the landing gear retracted and exited into the adjacent grass area resulting in substantial damage to the fuselage. The airplane was equipped with a landing gear position warning horn. The pilot stated that it was not wired through the intercom system, and that with his noise-canceling headset, it was rarely audible. The pilot reported that there were no mechanical failures or malfunctions of the airplane that would have precluded normal operation.