Fuel cut vs Ignition cut

You mentioned that there is also a fuel cut option versus the ignition cut. I know with the ignition cut, I'd have to worry about running rich and backfiring. However, with the fuel cut, would I need to worry about the engine running lean and running into knocking/pinging?

Also, do some tuners out there run these options simultaneously so that both the ignition and fuel get cut?

No, fuel cut is totally safe. It cuts a complete cylinder (or multiple cylinders) at a time to control engine speed. There is a small amount of fuel from the fuel film on the port wall that will still be drawn into the cylinder, however this won't be enough fuel to actually sustain combustion. Likewise there will be a brief period when fuel injection is reinstated where the cylinder will be slightly lean as the fuel film builds back up. Neither have proven to be an issue with using fuel cutting though.

Andre, what about a supercharger car with Nitrous, or a turbo charged car with Nitrous? Does fuel cut cause engine damage? Referring to traction control.

My preference is Ignition Retard -> Ignition Cut -> Fuel Cut. The use of retard first to remove torque is smoother, and I try to then have both the Ignition and Fuel Cuts at the same time, so that a lean cylinder isn't getting fired. The amount of fuel left available in the inlet manifold from the fuel film will vary greatly dependant on the engine, injectors, system temp and what the engines state was prior to the cut being enabled (i.e. a turbo charged engine with large injectors at full throttle is going to have a larger puddle formed than a naturally aspirated engine that has just come off of idle).

Using ignition retard for traction control is a nice option as it provides an instant torque reduction. The only thing I'd point out is the effectiveness is going to depend on how much torque you're needing to reduce in order to sustain traction (talking here solely with regard to traction control as opposed to launch control as per Joe's question). For example in most instances retard alone isn't going to be sufficient to control wheel spin so some form of ign/fuel cut will still be essential beyond the ignition retard alone. Also as you retard the timing the EGT will increase so if you're using a lot of retard and relying heavily on this for traction control, you'd want to keep this in mind.

@blackrex using a combination of fuel and ignition cutting simultaneously is great if the ECU provides that functionality, however in my experience the majority provide one option or the other so you're forced to choose the lesser of two potential evils. I've personally seen a few problems caused by ignition cut with engines that have problematic valve trains (SR20 jumps to mind), where as to date I've never seen engine damage that was contributed to using a fuel cut limiter. That's the basis for my recommendation although if you've got an engine with a well designed valve train and solid lifters, you're options are wider here.