The pilot reported that the engine began to run rough during cruise flight at 6,000 feet mean sea level (msl). He noted that the takeoff and climb were uneventful, and the personal instrument flight rules (IFR) flight had proceeded normally to that point. He advised air traffic control of the situation and elected to divert to an intermediate airport located approximately 10 miles west of his present position. The pilot increased the mixture, switched fuel tanks, and applied carburetor heat in an attempt to address the rough running engine; however, those efforts were not successful. The #1 cylinder temperature had dropped and the engine oil pressure subsequently went to zero. He notified the controller that he would be unable to make it to the runway and set up for a forced landing in a pasture about 3.5 miles east of the airport. The terrain consisted of rolling hills. After touch down, he was unable to stop the airplane before it impacted a fence and trees. The airplane sustained substantial damage to the leading edges of both wings. A post accident inspection revealed that the #1 cylinder exhaust valve had failed at the base of the valve stem. The intake valve and piston sustained mechanical damage as a result. The secondary mechanical damage precluded a metallurgical examination of the fracture surface of the exhaust valve stem. The Continental E225-8 engine that powered the airplane had accumulated about 1,130 hours since overhaul. The airplane had accumulated about 26 hours flight time since the most recent annual inspection, which was completed approximately one month prior to the accident.