It probably depends on the software but most of the time, those adware (as opposed to freeware or shareware) programs that you install look for specific files in order to function. These particular files are used to serve up ads through the software and are installed along with the main program. Some people equate them to parasites.
As an example, Kazaa, as you mentioned, requires the existence of a particular file (CL_CLINT.DLL, I believe), among many others, in order to function. Once Ad-Aware identified this file as a component of the spyware, its removal caused Kazaa to stop functioning.
For the most part, you're better off finding freeware alternatives to adware/spyware that you use if at all possible. It just seems the headache just isn't worth even installing these programs.