Most pilots with whom I have discussed ATC expected climb and descent rates are not aware they even exist. I discovered them long ago (1969) when I was browsing the Air Traffic Controllers handbook. You can find it today as FAA publication JO 71110.65T (effective February 2010). The prescribed specified climb and descent rates for your make and model aircraft are found in Appendix A of the handbook. See:
While operating your aircraft and Air Traffic Control issues a descent or climb clearance assure that you comply with the published rates. In 1997, the FAA notified 42 airline captains notices of certificate actions due to non-compliance with the published rates while climbing and descending. If you decide to descend or climb at a rate other than what is published, I suggest you receive a specific approval from your Air Traffic Controller.
Here is an excerpt from Appendix A of the entries for Cessna aircraft:
Climb DescentIf you are operating a Cessna C560, ATC expects you to climb at a rate of 6,000 feet per minute and descend at a rate of 3,500 feet per minute.