I currently work for a development company doing on call support and let me tell you there are 5 things I have learned that never seem to fail.  While some of them are tiny bit of an exageration ;) sometimes it seems like it happens allllll the time.

Problem Patterns
     Patterns don't really exist because once you find the pattern it immediatly changes before you can fix it.

Sleep
     If you do support at night sleep is what you day-dream about as the problems know EXACTLY when you are about to sleep.

Reboots
     Sometimes just rebooting the machine fixes the problem even when one "does" exist no matter the OS.

Remote Access
    VPN into the office only works on the small issues, you know the 5 minute fixes.  However, as soon as that HUGE 6 hours problem happens suddenly VPN isn't reliable if it even exists.

Life
    You no longer know what a "life" is as you need to be available at a moments notice to fix the problem because as soon you aren't available immediatly you get 5 phone calls from the higher-ups asking why you aren't on it yet.