This list is discounting legendaries.
Highest
HP
Blissey (255) Chansey (250)
Wobbuffet (190)
Wailord (170)
Alomomola (165)
Snorlax (160)
Atk
Rampardos (165)
Slaking (160)
Haxorus (147)
Rhyperior + Conkeldurr + Darmanitan + Archeops (140)
Salamence (135)
Def
Shuckle (230)
Steelix (200)
Cloyster + Aggron (180)
Bastiodon (168)
Probopass (145)
Sp. Ak
Chandelure (145)
Darmanitan-Z (140)
Alakazam (135)
Porygon-Z (135)
Volcarona (135)
Sp. Def
Shuckle (230)
Probopass (150)
Mantine (140)
Bastiodon (138)
Blissey (135) & Dusknoir (135)
Speed
Ninjask (160)
Accelgor (145)
Electrode (140)
Jolteon + Aerodactyl + Crobat (130)
Swellow (125)
Source
Lowest
HP
Shedinja (1)
Shuckle (20)
Dugtrio (35)
Mr. Mime (40)
Luvdisc (43)
Atk
Shuckle + Blissey (10) Chansey (5)
Smeargle (20)
Luvdisc + Darmanitan-Z (30)
Woobuffet (33)
Ledian (35)
Def
Blissey (10) Chansey (5)
Cryogonal (30)
Smeargle & Jynx (35)
Plusle + Accelgor + Beedrill + Sharpedo (40)
Drifblim (44)
Sp. Ak
Shuckle (10)
Smeargle (20)
Shedinja + Darmantian + Swak + Thorh + Sudowoodo (30)
Woobuffet (33)
Hitmonlee/chan/top (35)
Sp. Def
Shedinja (30)
Sharpedo (40)
Chatot (42)
Smeargle + Alomomola + Delibird + Cloyster + Wailord (45)
Ditto (48)
Speed
Shuckle (5)
Torkoal + Escavalier + Ferrothorn (20)
Gigalith (25)
Musharna (29)
Sudowoodo + Steelix + Parasect + Magcargo + Amoonguss + Slowbro + Sunflora + Reuniclus + Cofagrigus + Snorlax + Slowking + Bastiodon (30)
Source