The First Doctor

When The First Doctor enters the battlefield, search your library and/or graveyard for a card named TARDIS, reveal it, and put it into your hand. If you search your library this way, shuffle.
Whenever you cast a spell with cascade, put a +1/+1 counter on target artifact or creature.

The Twelfth Doctor

The first spell you cast from anywhere other than your hand each turn has demonstrate. (When you cast that spell, you may copy it. If you do, choose an opponent to also copy it. A copy of a permanent spell becomes a token.)
Whenever you copy a spell, put a +1/+1 counter on The Twelfth Doctor.

The Ninth Doctor

Haste
Into the TARDIS — Whenever The Ninth Doctor becomes untapped during your untap step, you get an additional upkeep step after this step.

The Thirteenth Doctor

Paradox — Whenever you cast a spell from anywhere other than your hand, put a +1/+1 counter on target creature.
Team TARDIS — At the beginning of your end step, untap each creature you control with a counter on it.

The Fifteenth Doctor

When The Fifteenth Doctor enters the battlefield or attacks, mill three cards. You may put an artifact card with mana value 2 or 3 from among them into your hand.
The first nonartifact spell you cast each turn has improvise. (Your artifacts can help cast that spell. Each artifact you tap after you're done activating mana abilities pays for {1}.)

The Third Doctor

Trample
The Third Doctor gets +1/+1 for each noncreature token you control.
When The Third Doctor enters the battlefield, create your choice of a Clue token, a Food token, or a Treasure token.

The War Doctor

Whenever one or more other permanents phase out and whenever one or more other cards are put into exile from anywhere, put a time counter on The War Doctor.
Whenever The War Doctor attacks, it deals damage equal to the number of time counters on it to any target. If a creature dealt damage this way would die this turn, exile it instead.

The Fourth Doctor

You may look at the top card of your library any time.
Would You Like A...? — Once each turn, you may play a historic land or cast a historic spell from the top of your library. When you do, create a Food token. (Artifacts, legendaries, and Sagas are historic.)

The Fourteenth Doctor

When you cast this spell, reveal the top fourteen cards of your library. Put all Doctor cards revealed this way into your graveyard and the rest on the bottom of your library in a random order.
You may have The Fourteenth Doctor enter the battlefield as a copy of a Doctor card in your graveyard that was put there from your library this turn. If you do, it gains haste until end of turn.

TARDIS

Flying
Whenever TARDIS attacks, if you control a Time Lord, the next spell you cast this turn has cascade and you may planeswalk.
Crew 2 (Tap any number of creatures you control with total power 2 or more: This Vehicle becomes an artifact creature until end of turn.)

The Eleventh Doctor

I. AM. TALKING! — Whenever The Eleventh Doctor deals combat damage to a player, you may exile a card from your hand with a number of time counters on it equal to its mana value. If it doesn't have suspend, it gains suspend.
{2}: Target creature with power 3 or less can't be blocked this turn.

The Fugitive Doctor

When The Fugitive Doctor enters the battlefield, investigate.
Whenever The Fugitive Doctor attacks, you may sacrifice a Clue. When you do, target instant or sorcery card in your graveyard gains flashback {2}{R}{G} until end of turn. (You may cast that card from your graveyard for its flashback cost. Then exile it.)

The Tenth Doctor

Allons-y! — Whenever you attack, exile cards from the top of your library until you exile a nonland card. Put three time counters on it. If it doesn't have suspend, it gains suspend.
Timey-Wimey — {7}: Time travel three times. Activate only as a sorcery. (For each suspended card you own and each permanent you control with a time counter on it, you may add or remove a time counter. Then do it two more times.)

The Second Doctor

Players have no maximum hand size.
How Civil of You — At the beginning of your end step, each player may draw a card. Each opponent who does can't attack you or permanents you control during their next turn.

The Fifth Doctor

Peaceful Coexistence — At the beginning of your end step, put a +1/+1 counter on each creature you control that didn't attack or enter the battlefield this turn. Untap those creatures.

The Sixth Doctor

Time Lord's Prerogative — Whenever you cast a historic spell, copy it, except the copy isn't legendary. This ability triggers only once each turn. (Artifacts, legendaries, and Sagas are historic. A copy of a permanent spell becomes a token.)

The Eighth Doctor

When The Eighth Doctor enters the battlefield, mill three cards.
Once during each of your turns, you may play a historic land or cast a historic permanent spell from your graveyard. If you do, it gains "If this permanent would leave the battlefield, exile it instead of putting it anywhere else."

The Seventh Doctor

Whenever The Seventh Doctor attacks, choose a card in your hand. Defending player guesses whether that card's mana value is greater than the number of artifacts you control. If they guessed wrong, you may cast it without paying its mana cost. If you don't cast a spell this way, investigate. (Create a Clue token. It's an artifact with "{2}, Sacrifice this artifact: Draw a card.")