I use all three types, although I use 3-flute centre cutting by default. For cutting accurate slots in one pass 2-flute cutters are recommended. That's possibly less important now with carbide cutters that are much stiffer than HSS.
It also depends upon the material. For aluminium, with high chip loads, I use 2-flute or 3-flute cutters to minimise choking of the gullets. For harder materials with lower chip loads, like steel, I use 4-flute cutters to maintain the metal removal rate.
I suspect that the introduction of 3-flute centre cutting tools has been largely driven by CNC, where they are a compromise between chip removal and overall metal removal rates. Centre cutting tools also make it much easier when engaging the workpiece with CNC than non-centre cutting.
Andrew