Meta: Everything about it

Oh, heck - let's just call the 40+ years it's been around a Crowning Lifespan of Awesome for the BBC, yes?

Ace

Ace beats the crap out of a Dalek with a baseball bat. Because it called her small. A specially empowered baseball bat, granted, but that makes it no less cool.

Meta: Russell T. Davies

Russell T. Davies successfully resuscitates the series after its cancellation in 1989 and failed return in 1996.

Meta: Episodes

Blink. The entire episode is made of awesome

The Master

"HERE! COME! THE DRUMS!"

The Tenth Doctor

The Doctor snaps and the TARDIS door opens. I mean, even he was impressed.

Captain Jack Harkness

After waiting for The Doctor for centuries, Jack finally finds him as the Doctor bolts via TARDIS. So Jack grabs on to the outside of the TARDIS. And holds on. As the TARDIS tries to ditch him. By going through time. And only stops when the TARDIS literally runs out of time to run through (because it reaches the end of the universe).

The Legionary in "The Pandorica Opens"/"The Big Bang"

Almost everything Auton!Rory does. In the latest series finale, there are so many amazing moments for this character, from punching the Doctor in the face and being complimented by him to defeating a Dalek temporarily with only an Auton handgun, saving the Amys and Doctor. By far the most awesome is guarding Amy for almost 2000 years, all alone- going so far as to pull the Pandorica out of a blazing building the Nazis have just bombed, knowing it will most likely kill him.

Rose Tyler

Rose Tyler/Bad Wolf to the Dalek Emperor: "You are tiny. I can see the whole of creation. Every atom of your existence and I divide them."

The Eighth Doctor

Subverting the behaviour of every action hero ever by, when cornered by a hostile police officer, swiping the officer's weapon and holding himself hostage. "Now, will you stand aside before I shoot myself?"

The Ninth Doctor

When, in "Bad Wolf", the Doctor promises to wipe "every single last stinkin' Dalek outta the sky!" despite having no weapons, no defenses and no plan — before promising Rose that "I'm coming to get you!"

Peri

Master: You will obey me! I am the Master!

Peri: So what? I'm Perpugilliam Brown and I can shout just as loud as you can!

Ace

Ace kills a Dalek with a rocket launcher. "I aimed for the eyepiece."

The Sixth Doctor

His Screw You, Time Lords speech towards the end of "Trial of a Time Lord" when denouncing the Kangaroo Court they set up to stop him from learning the truth about their corrupt dealings and atrocities:

In all my travels through time and space I have battled against evil. Against power-mad conspirators. I should have stayed here! The oldest civilization — decadent, degenerate and rotten to the core! Power mad conspirators? Daleks, Sontarans, Cybermen — they're still in the nursery compared to us! Ten million years of absolute power. That's what it takes to be really corrupt.

River Song

Say what you want about the character. But using a Dalek's own logic to make it repeatedly beg for mercy while calmly loading a gun to kill it in a single shot is nothing short of a Crowning Moment.

The Fifth Doctor

The "I'm not gonna let you stop me now!" cliffhanger to episode three of "The Caves of Androzani" — crash-landing a shuttle on the surface of a planet, mocking a mercenary who's threatening to shoot him if he doesn't stop it with the fact that he's already dying, and for added Fridge Brilliance stopping himself from regenerating right there and then — all to save the life of his companion Peri.

The Fourth Doctor

"Genesis of the Daleks". A Dalek chamber and a wire. "Do I have the right?" 'Nuff said.

Donna

Donna calls the Doctor out in the end of The Fires of Pompeii, allowing him to let just one family survive.

(duplicate example)

The First Doctor

Managing to convince virtually an entire audience that he is a brilliant harp player without playing a note in "The Romans".

The Second Doctor

His climatic speech to the Time Lords at the end of The War Games, about how they simply can't just sit back in the face of all the evils of the cosmos that he's faced.

The Third Doctor

Besting the Master in a sword fight in "The Sea Devils" and, in the process disarming him, holds him at swordpoint, stealing his lunch for no real reason other than to prove that he can, and then giving the Master his sword back because he's just having too much fun to stop. Oh, and then beating him again. Granted, the Doctor still ends up captured, but the entire sequence is pretty awesome.

The Seventh Doctor / Sylvester McCoy

For the Doctor, walking away from an exploding circus tent at the end of the "The Greatest Show In The Galaxy" without flinching. For Sylvester McCoy, walking away from that same exploding circus tent without flinching when he wasn't expecting the explosion to be quite that intense, because he knew they only had one chance to get the shot.

The Seventh Doctor

"Look me in the eye. Pull the trigger. End my life." Convincing two snipers to drop their weapons solely with the power of words.

The Second Doctor

His baiting of the increasingly delusional and megalomaniacal Eric Klieg in "Tomb of the Cybermen", complete with perfect capping-off put-down after Klieg reveals just how deranged and power-mad he is with a "I could rule the universe!" rant:

Well, now I know you're mad. I just wanted to make sure.

The Fifth Doctor

The scenes leading up to the regeneration in the final episode of The Caves of Androzani? Carrying Peri across a battlefield surrounded with explosions, nearly dying of asphyxiation in an earlier scene and generally engaging in derring-do - all so he can save the girl he accidentally got into this situation and all while dying from spectrox poisoning]. And not only this, but in the final moments of the first scene mentioned, he knows he has no cure for himself - he still delivers Peri to safety and meets death with dignity.

The Eighth Doctor

When the Master, having murdered Bruce, Chang Li, and Grace, brought the Earth to the brink of destruction and very nearly stolen the Doctor's remaining lives, leaps at the Doctor, but is blinded by the glare from one of the Eye of Harmony's mirrors, and flies into the black hole that powers the TARDIS. And as he hangs on for dear life — The Doctor reaches out and says, "Give me your hand."

The Master

In Utopia when Professor Yana opens his fob watch, to transform himself from human to something else? Who is he now, asks a terrified lab assistant?

"I. Am. The Master." (as tries to kill her)

Bonus awesome for being played by Sir Derek Jacobi, who is a extremely talented actor.

The Seventh Doctor

Driving the Godlike being Light to take its own life after Light has promised to eradicate all of life on Earth in "Ghostlight".

The Ninth Doctor

"The Long Game" - The Doctor revokes Adam's companion status.

The Fourth Doctor

"State of Decay" — defeating not only a coven of vampires but also the Last of the Great Vampires (a giant Eldritch Abomination buried under the planet) by launching a space ship that's almost out of fuel so that it rises, runs out of fuel part way through launch and falls right back down, thus both impaling the Great Vampire and wiping out the coven in one fell swoop. When it comes to this 'stake through the heart' business, the Fourth Doctor does not arse about.

Meta: SFX

The space station FX that opens Trial of a Time Lord.