I just upgraded to 13.04 on both my desktop and my laptop, but only my desktop is having this problem. It spontaneously hangs - I could be doing anything: trying to pull up the launcher, switching windows, clicking a link, typing an email - and becomes totally unresponsive (though the cursor moves) for anywhere from two to ten minutes. Sometimes it unfreezes and then freezes again a second later, sometimes it clears right up and performs fine for the next half-hour.
I've also seen a couple of errors - 'System program problem detected,' and an error related to (I think) usr/bin/Xorg that I haven't been able to replicate yet. These errors don't coincide with the hanging as far as timing goes.
I'm still pretty new to Ubuntu, so I'm learning my way around yet, but I'm picking up fast on the basics.