My understanding (but of course it may be wrong!)
S1 steering was off the Mini and often failed - guessing because of either heat or the weight of the engine or a bit of both! Many have 'upgraded' to the later electric pump (see below).
S2, S3 and S4 have similar systems and it is an electric pump that only draws current when it is asked to work ie. the wheel is being turned. This creates a slightly odd sensation as the effort required to turn the wheel reduces as the wheel is initially turned. The steering has been criticised but you do get used to it and once familiarised it actually works mostly quite nicely. My steering pump struggles a bit at very low speeds when turning the steering but this in only on grippy surfaces and I try to ensure the car is moving if possible to reduce the load. Steering has been very reliable although the fluid can get hot and leak out in extreme conditions.
The steering on late Aero derivatives was supposedly changed (improved) a couple of years back but I can't say I've noticed much difference on Plus 8s I have driven although the steering did seem rather meaty on the last car I drove. I liked it.