All the serious answers are correct in the general sense.
However there are specialist PCs that can boot without a graphics card and dump all the text data you normally get on screen to the serial port or via SNMP on the network. This means you can monitor a server remotely, especially in the later case. This can, in theory, mean you can completely manage a server from across the world. Couple that with an OS that can handle not having a graphics card, this means unix, linux, BSD, solaris, etc. and you can have a bunch of machines that don't have any graphics hardware at all, and can all be looked after completely from your bed via a laptop
With the domenance of comodity hardware these days in server environments, this is becoming pretty rare though. Especially as graphics chips or a couple of dollars to include on a motherboard. This wasn't the case 10 years ago.