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 this turn. Untap those creatures.

TARDIS

Flying
Whenever this Vehicle 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 Eighth Doctor

When The Eighth Doctor enters, 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."

Clara Oswald

Impossible Girl — If Clara Oswald is your commander, choose a color before the game begins. Clara Oswald is the chosen color.
If a triggered ability of a Doctor you control triggers, that ability triggers an additional time.
Doctor's companion (You can have two commanders if the other is the Doctor.)

River Song

Meet in Reverse — You draw cards from the bottom of your library rather than the top.
Spoilers — Whenever an opponent scries, surveils, or searches their library, put a +1/+1 counter on River Song. Then River Song deals damage to that player equal to its power.

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 token: Draw a card.")

Sarah Jane Smith

Whenever you cast a historic spell, investigate. This ability triggers only once each turn. (Artifacts, legendaries, and Sagas are historic. To investigate, create a Clue token. It's an artifact with "{2}, Sacrifice this token: Draw a card.")
Doctor's companion (You can have two commanders if the other is the Doctor.)

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 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 First Doctor

When The First Doctor enters, 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 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.