Rims start clicking when there's a developing spoke tension problem. Check for loose spokes by bouncing the shaft of a screwdriver off them and listening to their vibrating tones. A really low tone indicates a loose spoke and means the wheel needs retensioning.
Another possibility is that you have an old rim that was constructed using the pinned vs welded method at the seam and it's starting to come apart after many miles of being battered by potholes.
Last edited by Clem von Jones; 07-06-13 at 09:05 AM.