All R44s are governed. However, in my experience, it is one of the less reliable pieces of gear on the helicopter ( true on the R22 as well )
First of all, it's very easy for a pilot to inadvertently override the governor by simply holding the throttle too tightly. We see this all the time in a training environment. Being trained to keep a loose gentle grip on the throttle easily solves that problem. Some people fly with their hand back behind the throttle ( on the metal collective tube ) but I don't recommend that.
Additionally, any problem with the points in the right magneto can cause it to drop offline ( just stop working ) or to cause engine surging. I know several people personally that this has happened to. Depending on what's going on in this case, you may see incorrect engine tachometer indications because the tach works off the same points.
Also, the system can be affected by strong RF signals ( flying close to a radio transmitter ). I've seen this myself a couple times flying near FM radio transmitters.
The R44 has a mechanical correlator which moves the throttle when the collective is moved. The correlator works instantly, and then the governor fine tunes the throttle. At sea level, the correlator on an R44 will maintain RPM within a couple percent, even across large collective movements. At higher altitudes, or with a sick engine, the correlator will move the throttle too much, or not enough, and the governor will have to make an adjustment. Because the correlator moves the throttle simultaneously with the collective movement, while the governor is designed to make relatively slow corrections, rapid movements of the collective will cause momentary RPM excursions. Therefore, as in any helicopter, you should always make slow deliberate collective pitch changes.
Given that the governor on/off switch is right on the end of the collective, easily accessed by your thumb without having to remove your hand from the collective, there's really no reason why a governor failure of any kind should be more than a minor annoyance. People should have a good understanding of the difference between the correlator and the governor, the failure modes of the governor, and how to turn it off and finish the flight making manual corrections to RPM using the throttle. It really is not that difficult a system to master, however some schools don't include sufficient governor training resulting in some pilots who don't fully understand the system.