Do flight tracking websites also track non-commercial and defense aircraft?
As long as an aircraft transmits (unencrypted) ADS-B information, anyone within radio range can track it. The equipment necessary to receive ADS-B can be as simple as a computer with a TV receiver (USB DVB-T module) and the right software.

Receivers can then send the data stream to, for example, Flightradar24, who will display it on their website.

As Flightradar24 states, not all aircraft are equipped with an ADS-B transponder, and even those that do may not have switched it on. Unless ADS-B is installed and operating, it would not be visible.

@ezra-g mentiones that Steve Jobs' aircraft was blocked, but this is of something one would have to ask for, and the site has to apply the filter so it doesn't display on its website. However, Jobs' plane would still have been visible on the receiving computers. And, of course, the website will only filter your aircraft if they are willing to do so, either on request, through payment, or a government order.

Flightradar.com also has some other data sources, like FAA (Federal Aviation Administration) radar information in the US, which also contains aircraft without a transponder. The FAA may also filter some aircraft.