Panharmonicon

If an artifact or creature entering causes a triggered ability of a permanent you control to trigger, that ability triggers 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.

Annex Sentry

Toxic 1 (Players dealt combat damage by this creature also get a poison counter.)
When this creature enters, exile target artifact or creature an opponent controls with mana value 3 or less until this creature leaves the battlefield.

Court of Grace

When this enchantment enters, you become the monarch.
At the beginning of your upkeep, create a 1/1 white Spirit creature token with flying. If you're the monarch, create a 4/4 white Angel creature token with flying instead.

Sol Ring

Infested Fleshcutter

Equipped creature gets +2/+0.
Whenever equipped creature attacks, create a 1/1 colorless Phyrexian Mite artifact creature token with toxic 1 and "This token can't block." (Players dealt combat damage by it also get a poison counter.)
Equip {2}{W}

Archaeomancer's Map

When this artifact enters, search your library for up to two basic Plains cards, reveal them, put them into your hand, then shuffle.
Whenever a land an opponent controls enters, if that player controls more lands than you, you may put a land card from your hand onto the battlefield.

Rings of Brighthearth

Whenever you activate an ability, if it isn't a mana ability, you may pay {2}. If you do, copy that ability. You may choose new targets for the copy.

The Core

(Transforms from Matzalantli.)
Fathomless descent — {T}: Add X mana of any one color, where X is the number of permanent cards in your graveyard.

Matzalantli, the Great Door

{T}: Draw a card, then discard a card.
{4}, {T}: Transform Matzalantli. Activate only if there are four or more permanent types among cards in your graveyard. (Artifact, battle, creature, enchantment, land, and planeswalker are permanent types.)