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.)

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.

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.)

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

Bar the Gate

Counter target creature or planeswalker spell. Venture into the dungeon. (Enter the first room or advance to the next room.)

Dungeon Descent

Dungeon Descent enters the battlefield tapped.
{T}: Add {C}.
{4}, {T}, Tap an untapped legendary creature you control: Venture into the dungeon. Activate only as a sorcery. (Enter the first room or advance to the next room.)

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.