There are two things to consider.
1) Wear and tear on your computer. By turning your computer on and off multiple times a day you are causing your components to heat up(contract) and cool down(expand). This contractions, along with surging on and off your power supply has a cumulative effect on your computer. Think of a paper clip. The first time your bend it its fine, and you can bend it a bunch of times with no problems, however if you keep bending it, it does eventually snap. In general, keeping a computer running is better for the computer then repeated on/off cycles. In the business world it is a general practice to leave computers on all the time. Besides letting your computer update(which is usefull at home to) it also saves wear and tear.
2)Electricity usage. When your computer is on, its using power. This is a no brainer. It is not a huge cost( I think someone did an estimate and said 36 dollars a year) it does add up.
Now, saying all that, there are ways to leave your computer on and still save energy.
1) Turn off your monitor. Dont just leave it in standby, when you are away, just hit the button and shut it off. And if you still have a CRT monitor, replace it with a LCD. It is much more energy efficent.
2) Have your computer go into standby after a limited amount of time. Lets say 1 hour. But if you really want to conserve, you can have it shut off the disk after 20 minutes or so.
3) Make sure that your peripherals are only on when needed. Shut off your printer unless you are using it. Same with your usb hub or anything that gets plugged in. A lot of times people just leave there devices on even when not in use.
4)Shut it off at night, or when you go away for more then a day.
5)Plug all your devices ino a power strip. Now when you are done for the night, shut off the strip. This way nothing is left on. (always shutdown your computer properly first)
Finally, if you really want to know what the difference is in wattage for your computer over a period of time, think of getting something like this http://www.thinkgeek.com/gadgets/electronic/7657/ It is not very expensive and it will give you an exact reading of what is more energy efficient, and how much its worth. Just dont forget to include wear and tear on your computer in the calculations.