Lost Mine of Phandelver

Cave Entrance — Scry 1. (Leads to: Goblin Lair, Mine Tunnels)
Goblin Lair — Create a 1/1 red Goblin creature token. (Leads to: Storeroom, Dark Pool)
Mine Tunnels — Create a Treasure token. (Leads to: Dark Pool, Fungi Cavern)
Storeroom — Put a +1/+1 counter on target creature. (Leads to: Temple of Dumathoin)
Dark Pool — Each opponent loses 1 life and you gain 1 life. (Leads to: Temple of Dumathoin)
Fungi Cavern — Target creature gets -4/-0 until your next turn. (Leads to: Temple of Dumathoin)
Temple of Dumathoin — Draw a card.

Bident of Thassa

Whenever a creature you control deals combat damage to a player, you may draw a card.
{1}{U}, {T}: Creatures your opponents control attack this turn if able.

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.)

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.

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.

Tomb of Annihilation

Trapped Entry — Each player loses 1 life. (Leads to: Veils of Fear, Oubliette)
Veils of Fear — Each player loses 2 life unless they discard a card. (Leads to: Sandfall Cell)
Sandfall Cell — Each player loses 2 life unless they sacrifice a creature, artifact, or land. (Leads to: Cradle of the Death God)
Oubliette — Discard a card and sacrifice a creature, an artifact, and a land. (Leads to: Cradle of the Death God)
Cradle of the Death God — Create The Atropal, a legendary 4/4 black God Horror creature token with deathtouch.

Sword of Feast and Famine

Equipped creature gets +2/+2 and has protection from black and from green.
Whenever equipped creature deals combat damage to a player, that player discards a card and you untap all lands you control.
Equip {2}

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

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.

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.)

The Initiative

Whenever one or more creatures a player controls deal combat damage to you, that player takes the initiative.
Whenever you take the initiative and at the beginning of your upkeep, venture into Undercity. (If you're in a dungeon, advance to the next room. If you're not, enter Undercity. You can take the initiative even if you already have it.)

Undercity

You can't enter this dungeon unless you "venture into Undercity."
Secret Entrance — Search your library for a basic land card, reveal it, put it into your hand, then shuffle. (Leads to: Forge, Lost Well)
Forge — Put two +1/+1 counters on target creature. (Leads to: Trap!, Arena)
Lost Well — Scry 2. (Leads to: Arena, Stash)
Trap! — Target player loses 5 life. (Leads to: Archives)
Arena — Goad target creature. (Leads to: Archives, Catacombs)
Stash — Create a Treasure token. (Leads to: Catacombs)
Archives — Draw a card. (Leads to: Throne of the Dead Three)
Catacombs — Create a 4/1 black Skeleton creature token with menace. (Leads to: Throne of the Dead Three)
Throne of the Dead Three — Reveal the top ten cards of your library. Put a creature card from among them onto the battlefield with three +1/+1 counters on it. It gains hexproof until your next turn. Then shuffle.

Undercity // The Initiative

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.)

Dungeon of the Mad Mage

Yawning Portal — You gain 1 life. (Leads to: Dungeon Level)
Dungeon Level — Scry 1. (Leads to: Goblin Bazaar, Twisted Caverns)
Goblin Bazaar — Create a Treasure token. (Leads to: Lost Level)
Twisted Caverns — Target creature can't attack until your next turn. (Leads to: Lost Level)
Lost Level — Scry 2. (Leads to: Runestone Caverns, Muiral's Graveyard)
Runestone Caverns — Exile the top two cards of your library. You may play them. (Leads to: Deep Mines)
Muiral's Graveyard — Create two 1/1 black Skeleton creature tokens. (Leads to: Deep Mines)
Deep Mines — Scry 3. (Leads to: Mad Wizard's Lair)
Mad Wizard's Lair — Draw three cards and reveal them. You may cast one of them without paying its mana cost.

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.

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.)