The normal warranty model for PC's and their component is based off the 'Workspace' environment. Which is to say if a computer was constantly used 40 hours a week, every component would "work as advertised' for Three Years. So while you may be 'leaving it on' if your still having it 'work' (being a torrent server, running burn tests, etc.) while you were asleep, at work/school, etc. then it still would be 'constantly used' and thus 'decrease the life expectancy' guarantee (( as noted too would be sucking more cooler 'dust/hair' filled air and thus quicker to build up those dust bunnies that kill systems )).
So this doesn't mean the video card itself will suddenly burn out, or Windows will suddenly crash unexpectantly; but it increases the odds of any of the components (PSU to power every part, CPU, RAM, Hard Drives, GPU, motherboard, LCD screen, every fan, ANY plugged in peripherals, etc.) "life expectancy" shortening that one or may may go 'suddenly' and make it hard to diagnose the issue later on (see the numerous forum threads here where "Windows doesn't work' turns into PSU failing or RAM went, HDD Errors indicating failure, etc.).
Just weight the RISK ratio and know the expected outcomes, then plan appropriately to ensure your not 'screwed' because it happened at the worst possible time.