The best stable feud I can remember from wwe was DX vs nation of domination. It saw the rock and HHH blossom into complete stars and was entertaining even when xpac was fighting d-lo for the European? Title.
I know those two might not either one be the best ever, but they are both ranked high up there for me because of the memories of their feud.
My favorite stable of all time was the 4 horsemen though, back when arm Anderson could still wrestle. Not sure which version was my favorite, but they were booked well IMO and really knew how to draw heat in the ring. Helped to have really good baby faces to feud with like dusty Rhodes, sting, LOD, etc.