Vmware but very few hosting companies use it as it cost money for licenses compare to Xen & Openvz. You would pay a lot for hosting plans like that. Plus VPS are not just limited to Linux. You have windows as well for those ASP.Net sites.
There are many different types of VPS servers. Most providers offer two types of vps servers openvz and xen but there are a few more different types of servers. Every different type of vps server is built for certain requirements. Forexaple you may go with xen if you want nore power out of your resources instead of going with openvz for openvpn software.
All softwares are compatible and non compatible with different servers.
I dont know the exact number of different vps are out there but there must be a lot even some that we may of never heard of and are used for private use or even businesses that create their own stuff.
There are lots of different types of Virtual Private Servers. But, the question should be which are the more popular ones? And that answer according to the VPS wikipedia article is
Although VMware and Hyper-V dominate in-house corporate virtualization, they are less common for VPS providers, mainly due to cost and limitations - who typically use products such as: OpenVZ, Virtuozzo, Xen or KVM.
Then there are the different types of virtualization technology which I'm not going to go into detail about.