Cards that require other players to make decisions on turns that aren't theirs:
* Only in games with attacks
** Only in games with interactive cards
# Only complicated due to edge cases
^ Complicated due to reordering cards
Moat*
Bureaucrat
Militia
Bandit
Masquerade (although passing around the screen may be fun flavour)
Diplomat*
Torturer
(Saboteur)
(Smugglers is fine but game logs would be extra important)
Ghost Ship
(Possession is fine but perhaps a different wording would be more appropriate)
Watchtower**
Bishop
Contraband
Mountebank #
Rabble ^
Vault
Goons
Horse Traders*
Tournament (# for on play, but unambiguous for Followers)
Young Witch #
Duchess
Fool's Gold
Oracle ^
Tunnel **,#
Trader **
Mandarin **,#,^ (Only incompatible with Crown: if you gain a Mandarin on a turn that isn't yours and you have two of Crown, Overlord acting as Crown, and an Inherited Estate acting as Crown in play)
Inn **, # (very rare that you'd gain an Inn on a turn other than yours)
Margrave
Border Village **, # (see above)
Beggar *
Market Square **
Urchin
Catacombs **
Knights
Rogue
Hunting Grounds **
Advisor
Page (due to Solider)
Caravan Guard *
Duplicate **
Castles (due to Haunted Castle)
Catapult
Gladiator #
Crown **,# (Only incompatible with Mandarin in the circumstances listed next to it)
Legionary
(Mountain Pass requires passing around but it happens between player's turns)
Envoy
Governor (due to the Remodel option)
Stash **
(Band of Misfits, Inheritance and Overlord and Events are only issues with other cards on the list)
(Coin on the Realm and Royal Carriage are only issues with Caravan Guard)