There are a few things you can do before you drill it completely out.
Here are things I've done.
Cut off wheel - cut a nice side slot in the head of the bolt, or hammer a slightly smaller socket on and use a manual impact driver and the biggest flat-head bit (or the smaller socket)you can find..
This is BY FAR the most useful tool I have EVERY owned for my jeep. I cannot stress how many times this thing has saved my life. Every bolt I encounter (even the track bar bolts) I've hit 2 or 3 times with this thing and was able to get them off. I encourage everyone to get one of these.
Impact Driver- Craftsman-Tools-Auto & Mechanics Tools-Auto Specialty Tools
Weld a bolt to it - Many times I've welded or had someone weld another bolt to it and now you have another bolt to round off.
Extractor set - more difficult, but I've done it many times. Start by drilling a pilot hole with a small bit in the head of the bolt just a few 16ths deep. Then step it up to a manageable size you thing think the extractor can handle (torque)
12 Piece Screw Extractor Set
I have yet, and will never drill into a Tcase, diff, or engine for sake of a stripped head.