PanH got there before me, but I would very strongly recommend against using Hibernate at all, except for very specific occasions (perhaps a netbook/laptop where you need it near instantly available at irregular intervals but can't keep it always on for reasons of power). However, I realise some people like to use it, so feel free to ignore my discouragement.
A full shut down doesn't leave zombie remnants of past programs in memory (or at least probably restored back there from the hibernation file's copy of the memory state). Starting from a scratch screen of bare desktop with only whatever StartUp/registry-run TSRs you allow gives you a nice clean sheet, and you'll not be suffering from memory-leaks carried over from the last session. (You can set most browsers to restart the tabs that were last closed, if you have a complex set of websites you monitor. I know this from experience, having 27 tabs active in this browser, four 'active' in another (that I don't currently running, but which will start up on request), and 38 tabs in a third browser... although it looks like at least half of those are ones I shall prune before shutting it down next time, being not so important.)
It also lets you (when you choose to shut it down/restart, and let it do so) get the restart-necessary updates installed in a timely fashion rather than waiting until the rare times you restart fully (intentionally, or on an error, etc), and makes each process individually shorter and less harrying to your patience than the one big occasion when you find yourself "Updating 15 out of 25 updates", or somesuch, and wondering how many more are going to be several minutes'-worth more wait.
Or (mainly in XP era) find yourself with a "computer will restart in 15 minutes, unless you click here to delay this message for another 15 minutes" thing. Which invariable pops up while your computer is doing something complex (rendering or simulating) in the middle of the night and you're asleep at the time so wake to find the system restarted. (And the only official way to disable this behaviour is to disable to auto-updating system, of course. So you have to deliberately and manually initiate these and hope you don't get a "+1 day", as well as a zero-day, onto your system somehow.)
As for coming out of hibernate, randomly... Have you checked you haven't got Wake-on-LAN or Wake-on-Keyboard/Mouse active, such that something (maybe even a stray bit of electrical noise) persuades the notionally asleep machine to wind itself back up? (This might also apply to a powered-down computer, if still powered. But unplugging/turning off the wall switch would cure that as well. As it would for a hibernated machine, however so the switch-on might be being triggered.)