I used to have a 21" monitor here in my office a few years ago. My old cat BC used to sleep on top of the monitor: it was warm, it was big, and it was comfortable. He'd stretch out on top of the monitor and sleep for hours. Paws would dangle over the edge every so often and once in a while I'd have to move a leg so I could see part of the screen.
Yang would do the same thing. His tummy was always a lot bigger than BC's and he'd tend to lap over the edges in some less-than-dignified ways. Once in a while, I'd have two cats curled up on the monitor at a time.
When I went to a flat-screen monitor about a year ago, Yang came into the office once, looked at the flat-screen monitor, and tried to leap on top of it. This had about the result you might expect. He was grumpy with me for a while for having made him look foolish.
Bernie the Fuzzball has never known a CRT monitor. He's spending his time curled up next to the keyboard or halfway on top of it. I'm hoping to get him used to the idea of being charmingly round and somnolent nearby on the desk and not blocking the keyboard or mouse as he seems to prefer. However, he has found a place: stretched out on me, purring, and generally contributing to the writing process.