I've occasionally created home brew powers for my monsters, especially when it came to boss monsters.
Environmental attacks
I once created a Forge Golem who could pour molten steel into the arena, by pulling a chain on the ceiling. Each time this would shrink the size of the area that the players could safely fight in. He would also attempt to drop it on top of the players, especially if they were standing close together.
Feeding tube
I created a mindflayer boss once, who had some kind of wall mounted feeding tube attached to its back, that would heal him each round. Once the players figured this out, they first focused on severing the tube, before proceeding to deal damage to the boss.
Singing statues
The aforementioned Forge Golem was accompanied by four animated statues that produced a magical sonic effect that boosted the power of the boss. The appearance of the statues gave a clue to what their effect was. For example, a blindfolded statue caused melee attacks against the boss to have 50% miss chance. A statue with its mouth sewn shut, caused spells used against the boss to have 50% spell failure chance. An armored statue provided the boss with damage resistance. And the fourth and last statue, looked like a monk, and gave the boss regeneration. Bards could counter the effect of a statue with their music, and any silence effects of course also worked. However, since the statues were animated, they would of course attempt to get out of the area of effect of any silence spell. The players had to prioritize which statue to destroy first, and they had to split up to also keep the boss busy.