Should we reboot our servers?

The short but not very helpful answer is yes.  This article however trys to help you find the answers of how and when.  We at linuxinstall.net believe that it all depends on what the system can handle, what the business can accept, and when can take the system down.  It's rare that a system truly does have to be up 24x7x365.  Most normal situations call for outage windows which can be used to apply patches and reboot the systems.  You really probably should reboot a system, patches or not, around every 90-120 days.  That doesn't mean they can't stay up longer.  I had one system I choose to reboot every 180 days just to make sure it never hit the kernel bug at 368 days.  Even on Linux rebooting a system is healthy and tends to improve performance for the short run.  No matter what reboot your systems when it makes sense.