What steps can I take to diagnose a 2 - 3 year old iMac that is getting slower and slower. The CPU utilization seems ok, its just slow to respond. There is no obvious software running that would be slowing it down.
Create a new user account in System Preferences » Accounts. Do not copy anything over, but try to use that new user account for a few hours.
In case of hardware or OS issue:
Reinstalling the OS: If you use Time Machine, make sure you have a recent backup. Reinstall Mac OS X from scratch. If you don't use Time Machine, you should have an option to keep your user accounts and software. Otherwise, wipe it and restore user accounts and applications from Time Machine.
If none of the above steps help, you either have a hardware issue, or an imaginary problem (it happens).
Speedups for the hardware (in case your question title is your actual issue, not the description): More RAM, replace hard disk with SSD.