especially if they are left on for a long period of hours. (mainly speakin about my LCD of my laptop)

Theoretically, the Liquid crystal would start to fade and the colors wouldn't be as bright or vibrant as when brand new. But, assuming nothing else goes wrong, it would take years of continous use before you'd even notice it. You'd probable die of old age long before that happened (and that computer would probable be obsolete anyways).

Moniters are usually the part of the computer that last the longest.

Well the backlight can always go out...

We had a problem with the monitor connection on the Dell laptop for our portable CMM but not the monitor itself.

ps2wiz is 100% on that backlight thing. Seen many Laptop Displays with Backlight Tube failure. But as QWERTY said all of them were very old... 1995 486 Models or P1 models from 1997.