This is one of those questions that gets my favorite answer - it all depends. If you bought a white-box server with who-knows components, then you might run into problems with overheating of the CPU or hard drives. But if you bought a good-qualityname-brand server such as Dell, HP, IBM, etc., etc., then it should be configured to run continuously until doomsday (theoretically at least). Of course, over time, some hardware component may fail, thus bringing the server down, but other than that, there shouldn't be any problem with a server running continuously for months or even years at a time without ever being brought down for any length of time. This is, of course PROVIDED that you run it in a relatively clean and reasonably climate-controlled atmosphere so that the minimum and maximum environmental restrictions for the server are not exceeded on any regular basis.
Hope this helps!