Just about any! Depending on the underlying virtualization engine, you may or may not be limited in your choices. For example, an OpenVZ based virtual private server may be limited to certain Linux distributions where as a virtual private server running KVM virtualization, VMWare, Xen or Hyper-V may have a winder selection of operating system options including Windows (with a full desktop graphical user interface, just like your home computer may have).
We've written articles comparing the benefits of each popular hypervisor which is worth reading if you are just getting started.