Nadaar, Selfless Paladin

Vigilance
Whenever Nadaar, Selfless Paladin enters or attacks, venture into the dungeon. (Enter the first room or advance to the next room.)
Other creatures you control get +1/+1 as long as you've completed a dungeon.

Triumphant Adventurer

Deathtouch
During your turn, Triumphant Adventurer has first strike.
Whenever Triumphant Adventurer attacks, venture into the dungeon. (Enter the first room or advance to the next room.)

Yuan-Ti Fang-Blade

Deathtouch
Whenever Yuan-Ti Fang-Blade deals combat damage to a player, venture into the dungeon. (Enter the first room or advance to the next room.)

Thorough Investigation

Whenever you attack, investigate. (Create a Clue token. It's an artifact with "{2}, Sacrifice this artifact: Draw a card.")
Whenever you sacrifice a Clue, venture into the dungeon. (Enter the first room or advance to the next room.)

Fates' Reversal

Return up to one target creature card from your graveyard to your hand. Venture into the dungeon. (Enter the first room or advance to the next room.)

Barrowin of Clan Undurr

When Barrowin of Clan Undurr enters, venture into the dungeon. (Enter the first room or advance to the next room.)
Whenever Barrowin of Clan Undurr attacks, return up to one creature card with mana value 3 or less from your graveyard to the battlefield if you've completed a dungeon.

White Plume Adventurer

When White Plume Adventurer enters, you take the initiative.
At the beginning of each opponent's upkeep, untap a creature you control. If you've completed a dungeon, untap all creatures you control instead.

Dungeon Map

{T}: Add {C}.
{3}, {T}: Venture into the dungeon. Activate only as a sorcery. (Enter the first room or advance to the next room.)

Tomb of Horrors Adventurer

When Tomb of Horrors Adventurer enters, you take the initiative.
Whenever you cast your second spell each turn, copy it. If you've completed a dungeon, copy that spell twice instead. You may choose new targets for the copies. (A copy of a permanent spell becomes a token.)

Seasoned Dungeoneer

When Seasoned Dungeoneer enters, you take the initiative.
Whenever you attack, target attacking Cleric, Rogue, Warrior, or Wizard gains protection from creatures until end of turn. It explores. (Reveal the top card of your library. Put that card into your hand if it's a land. Otherwise, put a +1/+1 counter on the creature, then put the card back or put it into your graveyard.)

Enchant creature
Enchanted creature has flying and "Whenever this creature deals combat damage to a player, venture into the dungeon." (Enter the first room or advance to the next room.)

Midnight Pathlighter

Creatures you control can't be blocked except by legendary creatures.
Whenever one or more creatures you control deal combat damage to a player, venture into the dungeon. (Enter the first room or advance to the next room.)

Radiant Solar

Flying, lifelink
Whenever Radiant Solar or another nontoken creature you control enters, venture into the dungeon. (Enter the first room or advance to the next room.)
{W}, Discard Radiant Solar: Venture into the dungeon and you gain 3 life.

Ravenloft Adventurer

When Ravenloft Adventurer enters, you take the initiative.
If a creature an opponent controls would die, instead exile it and put a hit counter on it.
Whenever Ravenloft Adventurer attacks, if you've completed a dungeon, defending player loses 1 life for each card they own in exile with a hit counter on it.