I think this was asked before, but it's spread out into several questions. Rather than exclude the legendary, I'll give the best stat for the best legendary and the best nonlegendary. Also, B=Base, and M=Max stat.
HP - Blissey (B=255, M=714) / Giratina (B=150, M=504)
Attack - Rampardos (B=165,M=471) / Deoxys-A (B=180, M=504)
Defense - Shuckle (B=230, M=614) / Regirock (B=200, M=548)
Special Attack - Porygon-Z & Alakazam (B=135, M=405) / Deoxys-A (B=180, M=504)
Special Defense - Shuckle-(B=230, M=614) / Regice (B=200, M=548)
Speed - Ninjask (B=160, M=460) / Deoxys-S (B=180, M=504)