Leaving it on won't wear out any components within the amount of time that you're likely to own the system or actually put any of the components to use in any way. Only if they're already defective could it possibly do that, or if they're cheap and aren't designed to last long at all (sleeve bearing fans for instance).
Turning your computer on and off a few times a day also won't cause it stress to any degree that you would ever see a failure, unless something was already failing or defective. The expansion from temperature differences is minimal, not enough to cause extreme stress (perhaps using a peltier or extreme cooling may be enough to cause mild stress, but still, if you're doing that, you're not likely to be using the machine very long anyway).
The amount of your electrical bill increase from running a computer all the time is minimal, but it is there. I think someone once calculated it based on his rates and it came out to like 5 dollars a month. For a place like my house, that's a lot but it's spread across several people, we each have one computer (4 total, I'll soon have 2).
It all depends on what's worth it to you.
By keeping it on all the time, you have a greater chance of breaking the RC5 code or decoding the message from aliens with SETI@Home; you don't have to wait for it to boot every time you want to do something quick; you can run things like Napster and stay on AIM or ICQ all the time (if you have an always-on connection). However you also have to pay the extra electric bill and put up with any fan noise or hard drive noise (yes I can only think of two bad things about it).
By turning it off at night, you save a little bit of electricity and you can sleep without the constant hum of the fans and drive(s). But you also lose the RC5 and Seti@Home decoding time; anytime you want to do something after having shut it down you have to wait for it to boot again (can be annoying when you wake up in the middle of the night); if you turn it off more often, like whenever you're away for more than half an hour, it gets even more annoying to have to wait for it to boot just to do something quick (or even just when you want to do something NOW); you have to wait for things like AIM and Napster to load and connect; you don't get the constant hum of a nice big computer that you built yourself.
