Tomb of Horrors Adventurer

When Tomb of Horrors Adventurer enters the battlefield, 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.)

Nadaar, Selfless Paladin

Vigilance
Whenever Nadaar, Selfless Paladin enters the battlefield 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.

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

Radiant Solar

Flying, lifelink
Whenever Radiant Solar or another nontoken creature enters the battlefield under your control, 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.

Triumphant Adventurer

Deathtouch
As long as it's 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.)

White Plume Adventurer

When White Plume Adventurer enters the battlefield, 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.

Sefris of the Hidden Ways

Whenever one or more creature cards are put into your graveyard from anywhere, venture into the dungeon. This ability triggers only once each turn. (To venture into the dungeon, enter the first room or advance to the next room.)
Create Undead — Whenever you complete a dungeon, return target creature card from your graveyard to the battlefield.

Barrowin of Clan Undurr

When Barrowin of Clan Undurr enters the battlefield, 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.

Dungeon Delver

Commander creatures you own have "Room abilities of dungeons you own trigger an additional time."

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.)