To liken it to a car analogy: A taxi can do over 500,000 kilometers before it needs an engine rebuild. The reason for this is because they are always running, 24/7, and after a car’s engine is up to temperature, the amount of wear it receives while it is running is greatly reduced.
A computer is kinda the same. The majority of the “wear” on parts can happen when the server is booting up. Just attach an amp meter to your computer, and turn it on. When it starts up, the power it draws climbs very high, and then it settles down once all the disks have spun up and the processor is initalised. Also, think about how much disk activity the server undergoes during boot up vs when it’s working. Chances are the disk access from booting the OS is fairly solid activity, whereas when the OS is running, unless it’s a very heavy database server (I’m guessing not), the disks will most likely stay fairly idle. If there’s any time it’s going to fail, chances are it will be on boot up.
Turning your server on and off is a stupid idea. Not only to mention most servers can take upwards of 2-5 minutes to just get past the BIOS checks, it’s a huge amount of wasted time too.
2018 Update: Given that most computers are now essentailly entirely solid-state, this answer may no longer be as accurate as it once was. The taxi analogy doesn’t really suit todays modern servers. That said, typically you still generall don’t turn servers off.