How can I stop my garage door from hanging up on the door frame?
I would think the most likely candidate would be weakened springs.  The springs that support the door are ridiculously strong, but do loose their strength over time.  If they have weakened, the motor of your door opener has to lift more weight.  The heavier the load, the more likely it will be to hang up on something.  I would start by yanking the release rope on the door opener and lifting the door manually.  Does it hang in the same place?  Lube is definitely one thing to try.  I would also check all the hardware connecting the guide wheels to the door and make sure all the screws are tight.  

If the lube doesn't help and all the guide wheels are tight and it still hangs when opening manually, it's either a problem with the track or the springs.  You could inspect the track itself for debris or call a pro.  If you decide it is a spring issue, definitely call a pro.  Even a weakened spring is still very strong and can cause injury if not handled properly.

If the lube doesn't help and all the guide wheels are tight and it does not hang when opening manually, there is probably an issue with the automatic garage door opener.  They are relatively inexpensive and easy to install.