The problem usually comes from rounding out the hex head with the Allen wrench. It always seems like the wrenches are just not tight enough. If you don't know how to deal with this, a small job can turn into a huge headache! Here are some tips to help you prevent the problem in the first place and on how to deal with it, should it happen.

PREVENTION: Here is a list of things you should do to prevent rounding out a hex head bolt

Always thoroughly clean down inside the hex head hole. Use a pick or small screw driver to clean out debris.
The wrench must fit tightly all the way down into the head of the bolt. Don't use worn wrenches
Try to HIT the head of the bolt with a hammer and punch before attempting removal
This shock treatment helps to slightly loosen the grip of the bolt head to the surface
Don't use a slow turning motion with the wrench. This can actually increase the chance of rounding out the head.
Rather, use a quick snap or jerk of the wrench to break the bolt loose

CURE: If it still happens here are some options for bolt removal

If the damaged bolt is out in the open try grabbing the head with a pair of vise grips to loosen it.
As an alternative use a sharp chisel and hammer. Catch the edge of the head with chisel and hammer the head counter clockwise.
Use torx or star bits. This has become my favorite method. You may have to grind or modify the tip to get it to fit tight. See notes below:
If all else fails you will have to drill the head of the bolt off. Rent a right angle drill if space is limited.
Motor mount bolts (particularly 116, 123 and 126 chassis) - you can not get to the heads on some of these as they are up inside a hole in the subframe. If you can not get them out with a star socket or oversize hex then you will have to drill the head off and find a good used replacement motor mount arm...

NOTES on using socket drive Torx bits:

I always have a set of torx bits in my tool box of hex head bolt troubles. You need to find a torx bit slightly larger than the bolt head size. Then you can drive the bit into the head of the bolt with a hammer for a super tight fit. This may require that you modify the torx bit on a grinder. You can grind the sides off slightly or as in the picture below, you can grind off the tip to get the bit to fit tightly in the damaged bolt head. This really works. I love my torx!