A hypervisor needs to have the underlying hardware to support it. Specifically, it needs a lot of RAM, a lot of disk space, and a high-throughput processor (for which, see below).
As a first approximation, you can take the amount of RAM on a "standard" server and double it to get the amount of RAM you’ll need on a machine running a hypervisor.
Even more than RAM, hypervisors need disk space. Each virtual machine is running a copy of the operating system (which is often several hundred megabytes in its own right), as well as copies of any applications. This is especially true in server virtualization because servers are disk-hungry to begin with.
This is a consideration in other ways as well, notably when you’re exchanging virtual machines with someone else. A typical virtual machine is several gigabytes in size, too large to fit on a single CD-ROM. Even using a product like VM Optimizer from Invirtus or VMware’s shrink tool and zipping the resulting file, you still have a multi-hundred megabyte chunk to deal with.
This is why, for example, VMware’s virtual appliances are offered as downloads rather than on CD-ROMs. VMware cautions that a typical virtual appliance (virtual machine plus application) is about 2GB in size, and suggests using downloading software that can pick up where it left off in the event of a broken connection.
Counterintuitively, a modern hypervisor doesn’t take that much additional processing power. Most sources figure that the hypervisor architecture shaves a few percentage points off the application performance. Certainly the performance penalty is barely noticeable in most applications. (Gamers and graphics mavens, your mileage may vary.)