You really should leave the computer on 24/6 (doing a reboot or shutting it down once a week). Turning on and off the computer causes undue stress on components (esp. hard-drives which causes the most headache for people to lose!). Even overnight, the computer should be put into Sleep (aka Standby) or Hibernation mode, not turned off esp. if you are going to be turning it on the next day. It's sort of like a car: driving in the city with a lot of stop-and-go traffic is harder on the car and causes worse fuel efficiency than does driving at a constant speed along the highway. Some of the newer computers are very energy efficient now. They allow you to specify exactly what you want powered down and after how much time of inactivity (so I can have it switch to screen saver after 10 minutes of inactivity, turn off the monitor after 20 minutes., power down the hard-drives after 3 hours, etc.).
The difference between Sleep and Hibernate is that Hibernate mode will turn off more components and uses less power than Sleep mode. With both modes, all non-essential components are turned off (usually the monitor and other components like external hard-drives, web-cams, and some printers). In sleep mode, all data that resides on RAM will still reside there, and so some power needs to go into your RAM memory to maintain the current state of the computer. In Hibernation mode, however, all data residing in RAM gets stored onto the hard-drive. Thus it will take a little more time to wake-up a computer from Hibernation since it need to reload the RAM from the data stored on the hard drive. The Hibernating computer may still use some power, mostly to sense when the user wants to wake the computer up, but more components are able to power down in Hibernating mode, including the RAM and hard-drives. Also, a computer in Hibernation mode that has power disrupted can still reboot into the last state it was in, whereas in Sleep mode if power is disrupted, everything in RAM is lost and so the computer needs to reboot like normal (thus laptops that are not plugged in should be set to Hibernate instead of Sleep mode in case the battery dies before the unit can be plugged in again). Depending on the configuration, some computers will turn off network connections in either mode while others will only turn them off if in Hibernation mode to allow background transfers to occur in Sleep mode (eg anti-virus updates, etc.). Also different services may be kept running or turned off depending on how the Sleep mode is configured; most Server operating systems (eg Windows Server 2008) keeps all services running and network connections open since the server is usually not actively being used directly by an administrator, but rather indirectly by client computers which need the services and network running but not extraneous components like monitors etc.
There are a few things to be cautious about when setting computers to Sleep and / or Hibernation mode. Because both states keep the same state of memory between sessions, it is a good idea to reboot and / or shut-down the computer at least once a week. This will clear out the memory in case there are any lingering memory leaks from poorly written applications (esp. for the old version of Solitaire on Win 98 machines (I'm not sure about XP....)). Also, when saving the data to hard-drive in Hibernation mode will use any hard-drive space it finds instead of contiguous segments. Thus the hard-drive files will become more fragmented as a result of Hibernating the computer. So you should run the defragmentation application every few months to keep your hard-drive running at optimal speeds. Finally both modes keep an active power supply running so unless the system is plugged into some type of power surge protector, the computer should be turned off and unplugged (including any Ethernet cables plugged into it) during electrical storms (also disconnect cable / phone lines going into any modems to protect those as well).