Have

Basalt Monolith

Basalt Monolith doesn't untap during your untap step.
{T}: Add {C}{C}{C}.
{3}: Untap Basalt Monolith.

Don't Have

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.

Storage Matrix

As long as Storage Matrix is untapped, each player chooses artifact, creature, or land during their untap step. That player can untap only permanents of the chosen type this step.

Eye of Vecna

When Eye of Vecna enters, you draw a card and you lose 2 life.
At the beginning of your upkeep, you may pay {2}. If you do, you draw a card and you lose 2 life.

Sensei's Divining Top

{1}: Look at the top three cards of your library, then put them back in any order.
{T}: Draw a card, then put Sensei's Divining Top on top of its owner's library.

Howling Mine

At the beginning of each player's draw step, if Howling Mine is untapped, that player draws an additional card.

Getting

Winter Orb

As long as Winter Orb is untapped, players can't untap more than one land during their untap steps.

Isochron Scepter

Imprint — When Isochron Scepter enters, you may exile an instant card with mana value 2 or less from your hand.
{2}, {T}: You may copy the exiled card. If you do, you may cast the copy without paying its mana cost.

Walking Ballista

Walking Ballista enters with X +1/+1 counters on it.
{4}: Put a +1/+1 counter on Walking Ballista.
Remove a +1/+1 counter from Walking Ballista: It deals 1 damage to any target.

Island

Dramatic Reversal

Untap all nonland permanents you control.

Urza, Lord High Artificer

When Urza, Lord High Artificer enters, create a 0/0 colorless Construct artifact creature token with "This creature gets +1/+1 for each artifact you control."
Tap an untapped artifact you control: Add {U}.
{5}: Shuffle your library, then exile the top card. Until end of turn, you may play that card without paying its mana cost.

Aetherflux Reservoir

Whenever you cast a spell, you gain 1 life for each spell you've cast this turn.
Pay 50 life: Aetherflux Reservoir deals 50 damage to any target.

Hullbreaker Horror

Flash
This spell can't be countered.
Whenever you cast a spell, choose up to one —
• Return target spell you don't control to its owner's hand.
• Return target nonland permanent to its owner's hand.

Everflowing Chalice

Multikicker {2} (You may pay an additional {2} any number of times as you cast this spell.)
Everflowing Chalice enters with a charge counter on it for each time it was kicked.
{T}: Add {C} for each charge counter on Everflowing Chalice.

Sol Ring

Static Orb

As long as Static Orb is untapped, players can't untap more than two permanents during their untap steps.