Does Rabadon's only work when a spell or ability already does damage or even with effects that don't deal damage?

Rabadon's Deathcrown only works with spells and abilities that already deal damage. It does not add a damage component to effects that do not have one.

According to the official ruling (FAQ 0.72):

• Bonus Damage (like that granted by Rabadon's or Ravenborn Tome) increases each instance of damage something deals by X.
• If a spell or ability does not already have a "Deal" damage instruction, it has no damage instance to increase.
• For example, using a spell like Stupefy or Smoke Screen while Rabadon's is active will not cause those spells to deal 3 damage; they will still deal 0 damage.

Key Rules and Nuances:

• Rule 715: "Bonus Damage applies to the total damage Dealt by one instance of the action." If there is no "Deal" action, Bonus Damage has nothing to apply to.
• Rule 404.2: "Only Damage can be Dealt." Effects that modify Might (like -1 Might counters) or move units are not "Deal" actions and are not affected by Rabadon's.
• 0 Damage Events: You cannot deal 0 damage. If an effect (like Teemo's defense) results in 0 damage being calculated, no damage event occurs, and Rabadon's will not trigger to turn that 0 into 3 (FAQ 0.51).