There are two types:
- Type 1 which is what proxmox is. You can think of this like the hypervisor "is" the OS.
- Type 2 which sits on top of your host OS
Type 1 hypervisors:
- Linux KVM
- Proxmox
- VMware EXSi (not free)
There are a lot of others but these three are what I have experience with.
Type 2 hypervisors:
- Virtualbox
There are others like MS Hyper-V and Citrix but for me the list stops there. Virtualbox is the shit.