^^^^ Generally 50 yards or so for my 000 - 3 weight, about 75 for my 4 weight. From a practical standpoint, you may well not need it as "backing", just opens up the diameter of the loops within the reel so the fly line doesn't kink as much.
My notion .. if you can't fit 50 yards of backing with the fly line on the reel, you probably need a little bigger reel. With smaller stuff, 4 weight or less, if you're getting more than 100 yards of backing and your fly line on the reel, your reel might be big enough to off-balance the rod.
