* VMware ESX - enterprise grade virtualisation server. Combined with vmware infrastructure, you run a bare minimum hypervisor (no overhead from a standard linux or windows OS host), store your virtual machines on a SAN or NFS, have a pool of physical servers and automatically load-balance your VMs between them or even bring them back up automatically if a physical server goes bang. Nearly completely abstract your servers from the hardware, run 20 servers per actual piece of tin. Very much not free.
Almost. What you're describing is full "VMware Infrastructure". ESX is the bare-metal hypervisor - and has actually been "replaced" with ESXi. This is a stripped down version that has a smaller install footprint and therefore a lower exposure to exploits. Most of the old ESX patches were for things like Samba and CUPS on the service console. ESXi now comes from vendors like Dell in an embedded form even: 32MB on an SD card, pre-installed, no hard drive required.
You can use local storage with ESX and ESXi; just format it with VMFS. When you're dealing with live-migration (vmotion), automated resource balancing (DRS) and bringing VMs back up after a bang (HA), that's all part of VMware Infrastructure and Virtual Center.
Very much not free - BUT the ESXi installable hypervisor? Free. Go download it now if you want it. Due to the stripped down nature, it supports a more limited set of hardware than VMware Server (which relies on a regular host OS to work out the hardware details), but it performs much better. Depending on the host hardware and VM workload, you can get a 20:1 VM:host ratio with your eyes closed.
Disc space -- the final frontier!