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 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."

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 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 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.")

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.

Ace, Fearless Rebel

Nitro-9 — Whenever Ace, Fearless Rebel attacks, you may sacrifice an artifact. When you do, put a +1/+1 counter on Ace, Fearless Rebel, then it fights up to one target creature defending player controls.
Doctor's companion (You can have two commanders if the other is the Doctor.)

The Third Doctor

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

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.