Here's another thing that 'often' works for me.
First Step: Soak it with a penatrant, overnight would be nice!
Using a 'small' ball pein hammer tap the stripped head "gently" working the raised areas of the hex back down to the level of the rest of the head. This will do 2 things, first it will obviously take up area, making the hex smaller, second, it will 'shock' the threads, which often helps (especially with the use of penatrant) in the removal of a stuborn fastener. When you have worked the raised (stripped) areas back down, it's not uncommon that you will NOT be able to get the allen wrench back into the hex. Don't panic, this is the desired result. Now align the allen wrench (use a good one, if it is sripped, dress the end or throw it out) over the hex. With the hammer, "gently" tap the allen wrench into the hex of the bolt as deep as you can. Then try turning it out (counter-clockwise). Also sometimes depending on the size, you may be able to use the same process and substitute a 'standard' allen wrench instead of the metric, and vice- versa, depending on the application.
In my work, I try this first, then proceed (if necessary) to a center punch tapping it counter-clockwise, next step would be EZ outs / extractors.
GOOD LUCK