If you have programmes like your disc cleaner, defragger, various uploads and virus scans set to run at 2am or some such hour, it is best in this case to leave it on so these can be done (these checks are particularly important with older computers, as they help them run more effeciently).
If, however, you are content to have these run at some point during the day, it's generally best to turn the computer off to give it a chance to cool down (unless you have a MASSIVE heatsink in it). This is also very important for laptops, as the batteries get HOT even when plugged in.
Most people find it most convienent to run these tests/scans at night, as they do take quite a while and you're best not doing other things while they run in the background. I think the best option, for convience and for the sake of the computer, is to set all scans to run one day a week, starting at midnight and going every two hours from there (say disc cleanup at midnight, updates at 2, defrag at 4 so on and so forth) and only leave it on that one night a week.