Mine likes to loll atop the monitor on a cold day. Evidently he thinks it is a cat warmer. It's no problem until a tail drops down over the screen.

Trouble is, he became so attached to the computer that he started spraying it when the brainless neighbors let their cats out. (The cats come up to our door and sneer at him, driving him wild.) So I hung felt curtains over the affected area, and when he sprays, they go in the wash.

(For this and for other important reasons, keep your cats indoors.)

Despite the inconveniences, he is so affectionate that I wouldn't get rid of him for anything.