A desktop freeze is something that's not so rare nowadays - that's not good, but we shouldn't get desperate about that.
I like Compiz with Unity Desktop on my Ubuntu Trusty very much; I feel it's a step forward compared to traditional desktops. The only major nuisance I had on the previous versions was the inability to disable the global menu (which I like by itself, but I don't like the global menu disappearing when the mouse is not over it), but you can now disable it and have the menu on the window - even though you can't still enable an always-visible behaviour.
The problem is: compiz sometimes gets buggy. Running a different window manager, like metacity and/or xcompmgr just doesn't seem good, you can experience other issues and you're using the stack in a way it wasn't designed for. I don't like that approach.
So, what can you do when your desktop freezes? The symptoms are usually very clear: you can move your mouse, but you can't click nor type anything.
You don't need to reboot nor to restart X. You can fix this without losing your work.
Get a raw tty
Press Ctrl+Alt+F1 and get to a raw linux console, and login with your credentials. Make sure you use the same user you're logged into X with.
Find and kill your stuck process
This will print the PID of our stuck window manager.
Let's kill it
This won't usually be enough because the process is really stuck: if you repeat the pgrep command above, you'll find it still running - i.e. pgrep will return the very same PID as above.
So let's kill it, really this time!
pkill -9 compiz
Then wait some 15-20 seconds.
Now, if you repeat the pgrep , you'll either see a) no result or b) a different PID.
If you see a different PID, it's Ubuntu that noticed the crashed process and relaunched it; press Ctrl+Alt+F7, and you should just get back a working desktop!
If you see nothing with pgrep, you'll need to relaunch Compiz manually.
You cannot simply relaunch compiz on the console, because it must connect to X: the proper way to do it is:
Now switch back to your X instance with Ctrl+Alt+F7 and enjoy!