So, by default when you click on that corner we only have the ability to log-out of the system or suspend it, no hibernate or Shutdown functions are available. Although you can press the "Alt" key on your keyboard while accessing that menu which should change the "suspend" menu to "shutdown" (finally) but still, as far as I know you can't get that "hibernate" option.
This is typical Gnome behavior... although they do "explain" it by saying its their "job" to let users have the ability to control their desktop at its best, yet in truth...
Here's an important quote from one of the most prestigious software developers called, Joel...
"To make people happy, you have to let them feel like they are in control of their environment. To do this, you need to correctly interpret their actions..." Via: Joel on software.Now I may sound like an arrogant assho*$ but I'm not (okay, I do have a little pride me self as well :P). In fact, if you read that post you'll be amazed by the depths that Joel takes you which is hell of an article/insights.
But at the end (you'll understand this if you read it) nobody gives a damn about yours or mine's "freedom". But at the end, we are all driven by this primary need to control others using our own "means", even if it's visible in the most subtlest sense, one way or the other.
Okay, enough of this shit, let me get back to the topic (that actually rhymed :P)
So, if you're looking for a way to add both these functions into your Gnome3 or the shell (I'm using FC15 for this example), then we can use one of the plugins that comes as a part of the excellent Gnome shell extensions called "alternative status menu" which does exactly that.
yum install gnome-shell-extensions-alternative-status-menuThat's it. Now you should have both Shutdown and Hibernate options in that menu. Enjoy (I know you will :P).