Pokémon that can have the Run Away ability:

No.	Pic	Name	Type	Abilities	Base Stats
					HP	Att	Def	S.Att	S.Def	Spd
#019		Rattata		Run Away Guts	30	56	35	25	35	72
#020		Raticate		Run Away Guts	55	81	60	50	70	97
#077		Ponyta		Run Away Flash Fire	50	85	55	65	65	90
#077		Ponyta		Run Away Pastel Veil Anticipation	50	85	55	65	65	90
#078		Rapidash		Run Away Flash Fire	65	100	70	80	80	105
#078		Rapidash		Run Away Pastel Veil Anticipation	65	100	70	80	80	105
#084		Doduo		Run Away Early Bird	35	85	45	35	35	75
#085		Dodrio		Run Away Early Bird	60	110	70	60	60	110
#133		Eevee		Run Away Adaptability	55	55	50	45	65	55
#161		Sentret		Run Away Keen Eye	35	46	34	35	45	20
#162		Furret		Run Away Keen Eye	85	76	64	45	55	90
#190		Aipom		Run Away Pickup	55	70	55	40	55	85
#206		Dunsparce		Serene Grace Run Away	100	70	70	65	65	45
#209		Snubbull		Intimidate Run Away	60	80	50	40	40	30
#261		Poochyena		Run Away Quick Feet	35	55	35	30	30	35
#417		Pachirisu		Run Away Pickup	60	45	70	45	90	95
#427		Buneary		Run Away Klutz	55	66	44	44	56	85
#504		Patrat		Run Away Keen Eye	45	55	39	35	39	42
#827		Nickit		Run Away Unburden	40	28	28	47	52	50
#828		Thievul		Run Away Unburden	70	58	58	87	92	90
#831		Wooloo		Fluffy Run Away	42	40	55	40	45	48
#???		Dudunsparce		Serene Grace Run Away	125	100	80	85	75	55
#???		Tandemaus		Run Away Pickup	50	50	45	40	45	75
#???		Maschiff		Intimidate Run Away	60	78	60	40	51	51

Pokémon that can have the Run Away ability as their Hidden Ability:

No.	Pic	Name	Type	Abilities	Base Stats
					HP	Att	Def	S.Att	S.Def	Spd
#010		Caterpie		Run Away	45	30	35	20	20	45
#013		Weedle		Run Away	40	35	30	20	20	50
#043		Oddish		Run Away	45	50	55	75	65	30
#048		Venonat		Run Away	60	55	50	40	55	45
#265		Wurmple		Run Away	45	45	35	20	30	20
#290		Nincada		Run Away	31	45	90	30	30	40
#401		Kricketot		Run Away	37	25	41	25	41	25
#506		Lillipup		Run Away	45	60	45	25	45	55