Is it very bad for computers to be logged-on all night and in the middle of a game?

There are nine computers at my after-school care program and while I do my best to log off the computers each night and shut them down over the weekend, occasionally I forget . These are mostly flat-screen computers with hand-me-down parts and not particularly new. I do want them to last/work for as long as possible; what is best for the life of the computer? What is best for conserving energy? Is it very harmful to leave a computer on all night without exiting a game?