What an awful lot of fantasy heroes/heroines are addicted to is adrenaline. They're like bungee jumpers; can't resist the challenge of something a little more dangerous, more spectacular. Still, I suppose that's how you get to be a fantasy hero in the first place.
Does relying on some medication for survival count as an addiction? I'm thinking of Moorcock's Elric, who will die without a fairly frequent dose of somebody else's life force. A fairly typical vampire problem.
A few of the mortals who venture into faerie territory are held by sexual wiles; but prudishness in the copying has often left this as "hopelessly in love". And with faerie, you can never be sure there are no other enchantments involved.
Alcoholism in certain cultures is so universal as to make it practically impossible to be a hero without suffering from it (the morning after, at least). There again, the cultures from which the myths grew were very similar, and it wasn't considered as an addiction, any more than breathing, or eating.
Trouble is, the idea of addiction is fairly recent. Apart from lotus eaters, it's just assumed you've been enchanted in some way. Certainly, until you have broken the link between disease and magic, curses and misfortune, you are ill equipped to see that someone is 'wasting away' from substance abuse. If you are rich, and enjoy smoking opium, fine. If you are poor, you starve, and no loss. There are very few welfare states in fantasy.