One problem related to clunking noise has been reported for the 2004 Honda CR-V. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2004 Honda CR-V based on all problems reported for the 2004 CR-V.
2004 Honda Cr-v, problem started around 21,500 miles. I have a clunking sound when going over bumps or ruts in the road. More so if right front wheel hits a lower part of the road. Sounds as if something is loose. Still under warranty. Taken to dealer twice. They replaced strut and second time moved the engine mount over. It did not help. Sounds as though metal clunking against metal. Will take to another dealer to see if they can find the problem.