Under ideal conditions it is better to leave the case cover on. However most people do not keep their computers under ideal conditions! Most home pc's I see are on the floor (sometimes carpeted) or jammed under a desk against the wall (sometimes even in a small cutout in the desk w/no rear ventilation at all). These conditions can actually create more heat with the case cover on as there is no adequate supply of cool air available to intake (don't even get INTO not cleaning filters on fans that have them!). In situations like this, the case cover off combined with a good quality heatsink fan combo will actually exahst hot air to the room and draw in cool air from the ambient room which will be cooler than the hot air that would have been trapped inside the case.
That being said, the matter of should you keep the pc in the case really depends on the design of your cab. Remember, the purpose of intake and exahst fans in a pc case is to draw in cool air and get rid of hot air, if your cabinet performs this function and the air inside is relatively cool (and this should be a consideration, not only for the health of the pc but the monitor as well) you may be able to get away with leaving it in the case (as this would be convienent for most users). if the air in the cab is substatially warmer then the abient temp, you may be better off adding a couple of fans to the cab and pullin the pc out of the case.
Regardless, try to keep the PC at the bottom and make sure there are some vents to let in cool air at ground level.
(also keep in mind that all cpu's aren't created equal and some get a lot hotter than others (as well as being more or less susceptable to thermal failure))
-C