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.)

Trophy Mage

When Trophy Mage enters, you may search your library for an artifact card with mana value 3, reveal it, put it into your hand, then shuffle.

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.

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.)

Trinket Mage

When Trinket Mage enters, you may search your library for an artifact card with mana value 1 or less, reveal that card, put it into your hand, then shuffle.

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

Delver's Torch

Equipped creature gets +1/+1.
Whenever equipped creature attacks, venture into the dungeon. (Enter the first room or advance to the next room.)
Equip {3} ({3}: Attach to target creature you control. Equip only as a sorcery.)

Immovable Rod

You may choose not to untap Immovable Rod during your untap step.
Whenever Immovable Rod becomes untapped, venture into the dungeon.
{3}{W}, {T}: For as long as Immovable Rod remains tapped, another target permanent loses all abilities and can't attack or block.

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.)