We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multiparticle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as between squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gaslike and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.