From a physics standpoint, the minimum is zero. It is physically possible that if everything were lined up correctly that the launch vehicle's ascent takes it directly to the destination.
From an engineering/planning standpoint, things are much harder. You don't have perfect information or control, so you approach in stages. For a question about approach to the ISS, see Steps between rocket launch and docking on Space.SE
Is the number highly variable between missions? I presume higher altitude satellites require more orbits to reach.
In order to change your orbital distance to an object in your plane (phasing), you need to be at a different altitude. Unless you have extra fuel to burn, you don't want to fly above it, then back down when you get there. And you have to be above the atmosphere. So there's little room to play with for lower-orbiting satellites. The higher the target orbit, the slower it will be orbiting and the faster you can catch up to it.