Elesh Norn, Mother of Machines

Vigilance
If a permanent entering causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.
Permanents entering don't cause abilities of permanents your opponents control to trigger.

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.

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.

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.

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.)

Veteran Dungeoneer

When Veteran Dungeoneer enters, venture into the dungeon. (Enter the first room or advance to the next room.)

Cloister Gargoyle

When Cloister Gargoyle enters, venture into the dungeon. (Enter the first room or advance to the next room.)
As long as you've completed a dungeon, Cloister Gargoyle gets +3/+0 and has flying.

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.