I'd have to say... maple is my favourite backing. I've backed cherry, yew, ipe, osage, jatoba, and yellowheart with maple, and all have turned out well. And, every imaginable design... ELBs, warbows, flatbows, bendy handles, long, short... you name it. To top it all off, it makes a great (lighter weight... up to 50#) flat pyramid selfbow, too. Another fav of mine is rawhide backed maple.
As far as thickness goes... usually 1/8", but I've used up to 3/16" on maple backed yew warbows up to 120#. Of course, like any other backing, it's all about the grain.