There is no conclusive evidence to suggest that leaving a laptop on all of the time causes any damage to the system. The monitor or screen can be damaged by persistent images, but settings such as power-saving and screen-savers prevent this in long-term usage.
Laptops generate a lot of heat but do not overheat while not in use, as processor demand and video card usage causes the heat build-up. The biggest reason not to leave a computer on is to conserve power. Laptops in particular use settings such as sleep mode and hibernation mode to offset some of their power consumption, while providing a quicker boot-up.