This isn’t strictly a “counter”, but it’s absolutely something to watch out for. Had enough of your opponent’s smug Ambassadors, showing up at your door with unwanted Estates and Coppers? Simply Possess him, then watch him howl with fury as you Ambassador away two of his Colonies and hand one out to everyone else in the game. In a two-player game, this can result in a 30VP swing! In multiplayer games, it is the only way to permanently remove cards from an opponent’s deck with Possession (since it doesn’t count as “trashing”) to directly benefit yourself, and it is a vicious counter to one of the most effective early-game attacks.
In a two-player game, Masquerade is a good substitute, though slightly less effective (since you can only cost the player one card instead of two). In a multiplayer game, the Possessed Masquerader will be passing cards to someone other than yourself, so you can hurt the Possessed but not help yourself.