I have good luck with cobalt left hand  drill bits.  Rick

Yep LH bits run in reverse, otherwise you won't get much done  sorry!  They usually come with a decent extractor set, or at least the ones I buy do. Get a good enough bit and like everyone said you can drill out just about anything including the broken easy out. Like Dwright said use a bit that's just under the size bolt about 1/8" under. Use a punch to get started, take your time, don't go too deep, make sure your dead on so you don't cut the the threads and 9 times out of 10 you will be good to go. Having a high rpm drill helps a lot but you can get by fine with a cordless if you have a decent bit.