3) Any combination of the following that has at least one of the "limited use" cards in it.
Limited use
Action cards that trash cards from your hand to work: Moneylender, Remodel, Expand, Remake, Treasure Map, Develop, Stonemason, Transmute, Trader, Taxman, Mine, Trading Post and Procession
Action cards that remove cards from you hand other ways: Island
No use
Actions that ITR has no effect on: Secret Chamber, Tactician, Outpost, Library, Watchtower, Chapel, Counting House
Non-Actions: All
Depends
Multipliers limited by your hand: Throne Room, King's Court
(Allow playing more than one different card in a turn, which is only relevant if you play with Shelters OR there is a card that does not require you to lower your handsize to do something. Those cards include "no use cards" that still don't get additional benefit from being played by ITR)
Honorable mention:
Rats (which gives actions and cards but doesn't make the card "broken" for obvious reasons)
Edit: Forgot that Procession is a tfb itself and should be in the "limited use" category rather than "no use". Probably the effect isn't really useful most of the time, but nonetheless.
Edit:Removed Forge, Salvager and Altar due to Holger's remark.
Edit: Made a category for TR and KC that can add flexibility (in some cases)