Showdown! already has a format where Pokemon can have illegal abilities. Seeing how it's so successful, I think all the broken abilities have already been banned. These are the banned abilities: moody, shadow tag, power construct, arena trap, comatose, contrary, fluffy, fur coat, huge power, illusion, impostor, innards out, parental bond, protean, pure power, simple, speed boost, stakeout, water bubble, wonder guard
The most broken ability/Pokemon combination that isn't yet banned is regenerator on Pokemon that know u-turn or volt switch.