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.