The main theme of the series has always been awesome in all of its various incarnations (including the one for the movie, even if it sticks out like a sore thumb compared to the rest of them).
Special kudos to the version for Tom Baker's final season, as well as Peter Davison's run and Colin Baker's first season, with the synthesizer that sounds suspiciously like an electric guitar solo. That's right — the awesomeness of the Doctor has been enhanced by The Power of Rock.
Actually, most stuff by Chameleon Circuit deserves an honourable mention on this page. It might not be actually heard on the show, but it's all one great big celebration of everything which makes the show awesome.
Televised Doctor Who
That plain leitmotif for the city in The Daleks.
The background music during the Daleks' fight with the Mechanoids at the end of The Chase is also pretty awesome.
From The Time Meddler, the plainchant that the Meddling Monk puts on to create the illusion of many actual monks.
The music that plays over the Blind Man's Buff games in The Celestial Toymaker, especially how they harmonize with the buzzers.
The soundtrack for The Invasion, a cross between a soundtrack from a western with one from a spy thriller.
That motif that plays over the film trims of the pirates planting the charges in The Space Pirates.
The Ambassadors of Death has a catchy synthesizer tune which shows up a few times and can be heard in its entirety in episode 2, when the UNIT convoy drives Recovery 7 back to the space center.
And check out this "UNIT theme" also from "Ambassadors of Death".
Everyone seems to hate the "Sea Devils" soundtrack, calling it a glorified series of electronic fart noises- listen to this arrangement, which captures the most eerie parts of the music and avoids the least well-regarded snippets.
The music in The Androids of Tara, especially that absolutely gloomy wedding march in Part 4.
The fabulous, Gershwin-inspired "running through Paris" music from City of Death.
The score to Logopolis.
Although it was really just a simple bit of 80s incidental music, the haunting "flashback" music that plays as the Fourth Doctor is seeing the images of his old enemies taunt him before he falls is unforgettable.
...And the slow descent of single synthesiser tones down a minor scale as we see him lying on the floor just prior to regeneration. Very simple and yet very effective.
The cool 80's music playing while K-9 travels through the forest in Full Circle.
The score to Castrovalva.
The score to The Visitation is a real gem, and it's a shame that it's so hard to find.
All of the music from Mawdryn Undead was fantastic, making it even more amazing than it already was.
Planet of Fire had an atmospheric soundtrack for many of the scenes set on Sarn.
Season 23 / The Trial of a Time Lord
The opening music from the first episode of "Trial of a Time Lord", with the epic computer-controlled whirling shots of the Time Lord space station, all done with model effects that, in a rare moment for classic Doctor Who, still hold up as excellent today-watch it here. Definitely the best bit of "Trial of a Time Lord" and the most expensive special effects done on the original series (it shows).
The soundtrack from Remembrance of the Daleks is '80s-licious, especially the bit (0:00 - 1:15) where Seven and Ace are tearing down the street with the Daleks hot on their heels.
The soundtrack to The Greatest Show in the Galaxy.
The epic guitar riff from Survival that plays on the cheetah planet.
The final peice of music in the classic series (apart from the theme) as the Doctor and Ace walk away.
A good portion of the TV movie soundtrack falls into this, more specifically "Breakout", "The Chase" and "Open the Eye".
Series 1 / Season 27
"Rose's Theme". Especially when it plays at the end of "The Stolen Earth" when the Doctor and Rose see each other for the first time in years.
"The Lone Dalek" Not only was it beautifully used during the episode "Dalek" but it was AMAZINGLY used at the end of "Doomsday" (admittedly, most people assume that the last piece of music in that episode is Doomsday or Rose's Theme). But when the music reaches its final climax JUST as the tear falls down the Doctor's cheek as he finds himself alone in the TARDIS at the end...it also has the benefit of providing another point of comparison for the Doctor and the Daleks that a song about a Dalek's loneliness can be used so effectively for the Doctor. This piece of music is one of the most beautiful and haunting pieces of music EVER.
"The Impossible Planet". Some rather scary, mournful strings, evoking the ancient and impossible setting of the episode of the same name well, before turning to a more emotional piece of Murray's midway through.
"Doomsday", from the episode of the same name, contributes just as much to the Tear Jerker ending as the acting.
That song was used in the final few minutes of "Turn Left". As the Doctor questions Donna on the alternate reality that had been built around her, the music is soft and in the background. Then when she talks about Rose, the music picks up, and when Donna passes on the message, "Bad wolf", the music picks right the hell up and punches you in the gut. It's fast and crazy and can't help but get your heart pounding.
The scene in question, you can clearly see how the music builds up with the Doctor's Oh Crap face.
Also used to great effect in The End of Time as the Doctor finishes his frantic race back to Earth to face The Master and Rassilon.
Behold this bassoon-eriffic, subdued version from the 2010 Proms—followed by the magisterial "Vale Decem" no less, and showing footage of all the Doctor's regenerations. Extra points for the audience's standing ovations at Pertwee, Tom Baker and Tennant.
Starting "Vale Decem" 2 seconds before "This Is Gallifrey", and playing with the latter's volume just a bit at times, produces a heartrendingly beautiful song. They play off of each other really well... the beginning is a little discordant, but it soon resolves. For example: the swell in T.I.G. at ~1:45 - it's perfectly mirrored in Vale Decem, and that's only the most prominent matchup.
The "Voyage of the Damned" suite from the Series Four soundtrack. In particular, three passages: Astrid's Theme followed by a Braveheart-flavoured rendition of "The Doctor Forever"; the reworking of "All the Strange, Strange Creatures" as the Titanic falls before rising into a glorious instrumental of "The Stowaway"; and the finale with the Doctor's goodbyes to Astrid and Mr. Copper.
How awesome did Donna Noble turn out to be? This track sums it up nicely. Seriously, it sounds like the sort of music that would be playing if the girls from Sex and the City were out saving the freaking universe.
"The Rueful Fate of Donna Noble"; Donna's decision to go to her death in "Turn Left". The latter is reprised with Donna's final sacrifice in "Journey's End"; and it's even been bolstered with the riff from "Doomsday".
"Turn Left" got one of the most chilling themes ever, combining all sorts of recognizable snippets into one haunting piece that NEVER gets old. EVER.
"A Dazzling End" is the music played in "Turn Left" as Donna chooses to sacrifice her potential future self to save her potential past self so that her life with the Doctor continues to exist.
In "Journey's End," when the TARDIS is towing the Earth back home, there is some truly, truly awe-inspiring music: the "Song of Freedom", the Oodsong writ large and glorious as the "Song of Freedom". Ten minutes later, however, and it's back to being a Tear Jerker. 5 years after "Journey's End", Murray remains the maestro of this show.
"A Victorian Christmas". A beautiful, epic Christmassy theme...interrupted by the sweeping jazzy entrance of "the next Doctor".
The Cyberman theme from series 2 turns into a dark march for "The Next Doctor", ending with a rousing hint of "The Doctor Forever".
In "The Waters of Mars", a fast-paced, action-oriented piece of music begins to play in the climactic scene of the episode, continuing on until the base explodes at the end. It's such a fitting piece that pretty much defines the urgency and heroic nature of the situation.
"The Council of the Time Lords", a short, dark, and utterly awesome version of "This is Gallifrey" plays at the beginning of Part 2 of "The End of Time". The song, along with Gallifrey's ruined, Dalek-saucer-littered landscape, gives an inkling of just how twisted and desperate the Time Lords have become in the last days of the Time War.note And yes, the resemblance to The Imperial March from Star Wars is intentional. Apparently.
Breaking news, from the "Final Days" of Planet Earth: the Master is everyone. The second half of the piece also serves as the true gamechanger of "The End of Time Part One"'s cliffhanger: the Time Lords are returning, and the narrator is the President of the High Council.
From "The End of Time" part two, "The Clouds Pass", the music that started up when the Master told the Doctor to get out of the way. That was pure badass. And it's a heroic sounding theme, used for the Master, without feeling the slightest bit out of place.
"The End Draws Near", from "The End of Time" Part One, another soft, emotional Tennant piece that increases into a Time Lord march.
"Vale Decem", the song sung by Ood Sigma for the Tenth Doctor. Translated as "Farewell Ten", it's in Latin, and it is actually a true goodbye to the Tenth Doctor. Apparently this translation is a bit rough and inaccurate, but it's close enough for us to get the overall meaning. That made the scene even more meaningful. If it was a Tear Jerker before, it's even more now.
"We will sing to you, Doctor. The universe will sing you to your sleep."
The rousing choral crescendo that plays as the Tenth Doctor begins to regenerate in the TARDIS. It's a reprise of "The Doctor's Theme" that's been with us since "Rose" in 2005, but it manages to be bombastically triumphant and desperately sad at the same time.
What makes it even more awesome, is that even though the song is sung in a different language, you can hear the singers say the phrase, "God save the TARDIS".
Two more saddening and heart-wrenching tracks from David Tennant's final moments: Four Knocks and this reprise of "Song for Ten".
Even more heart-wrenching when you consider the fact that the last thing the Doctor said before Wilf knocks was his astonished statement of "I'm still alive."
"Down to Earth" is a sweeping big bang of an action theme that starts off series 5 pretty well.
The Eleventh Doctor's theme — "I Am the Doctor" (Version from the 2010 Proms included, for extra goodness). It sounds like the orchestra managed to purify badass down to its essence, drenched their instruments in it, and just started to rock the hell out. You know things are about to get intense.
It's also played over particularly dramatic moments and trailers (like this one), thumping you upside the head to say "This is goddamn epic!"
"A River of Tears" is not only a very haunting piece, it also features backmasked sections, which symbolise River's relationship with the Doctor, always meeting in reverse order. And if you play it backwards you get a similar piece that sounds a little darker and more intense...
"You and Me, Amy" is a sad remix of several series 5 pieces, before closing with a quiet, soft piece.
"The Patient Centurion" is lovely. Listen closely and you'll hear a slower, more melancholy version of the melody in "I Am The Doctor".
"I Remember You" plays over the climax in "The Big Bang" at Amy's wedding. It's, in a word, triumphant.
Series 6 / Season 32
"Abigail's Song" from "A Christmas Carol". Haunting, beautiful, and with a slight suggestion of the Arc Words "Silence will fall".
"The Majestic Tale (Of A Madman In A Box)", the epic, triumphant variation of "I Am the Doctor" that plays as the Doctor defeats the Silence and River's ensuing ass kicking of said Silence in "Day of the Moon", and as all 13 Doctors save Gallifrey in "The Day of the Doctor".
"Brigadier Lethbridge-Stewart" is an amazing piece starting out small and sad, yet quite beautiful as the Doctor finds out about one of his oldest and best friends' death, then builds up to an awesome arrangement of I Am The Doctor that captures the bittersweetness of revisiting the events of The Impossible Astronaut and the death of the Doctor from the Doctor's perspective.
Series 7 / Season 33
"Bah Bah Biker", a catchy tune that plays while the Doctor and Clara ride to the cafe in "The Bells of Saint John".
"The Long Song", the hymn the people of Akhaten sing in "The Rings of Akhaten" while trying to quell the sentient sun.
"The Name of the Doctor Suite", starting off with a Triumphant Reprise of "This is Gallifrey", (known as "To Save the Doctor") bringing to mind the image of the Gallifrey of the Doctor's youth, with the Time Lords at their very height.
"Remember Me", starting with Clara's emotional piano Leitmotif before building in an epic variation of "I Am The Doctor", which plays at the end of both "Asylum of the Daleks" and "The Name of the Doctor".
"Infinite Potential", a moving instrumental of "The Long Song", which plays as Clara sacrifices her leaf in "The Rings of Akhaten", and as the Eleventh Doctor delivers his dying speech in "The Time of the Doctor".
There is the very triumphant and very epic rearrangement of "This is Gallifrey" that plays as the Eleventh Doctor starts his regeneration, which then segues into a very epic arrangement of "The Doctor's Theme (Series 4)".
"Trenzalore", a low-key, tragic recurring theme based around the Doctor's fate on the planet Trenzalore heard in "The Name of the Doctor", "The Day of the Doctor" and "The Time of the Doctor".
"Always the Doctor" is a beautiful arrangement that features several different insturmental beats, including The Long Song and Infinite Potential. While the 10th Doctor's theme was a choir singing of his funeral hymn, this is a gentle lullaby to sing the Eleventh to sleep. It ends with the first hint of the 12th Doctor's Theme.
"Captain Jack's Theme". Pure. Win. Even better, it crops up in the aforementioned "Owen Fights Death". The companions' themes in the Who series tend to be softer, more melodic tunes, but Jack's is exactly the opposite.
Jack's theme becomes even more awesome when you learn that it was written for the end of Countrycide, and is structured around repeated use of the phrase, 'Here he comes in a bloody great tractor.' Which is just kind of hilariously brilliant.
It becomes even more awesome when you realise that as Jack has become more like the Doctor, at 1:08, it's segued into "The Doctor's Theme" and then at 2:00 the melody seems to be a riff on "This is Gallifrey".
"Torchwood Theme" from the credits is pretty cool too. The use of the pattern from "Army of Ghosts" is a pretty neat touch. Also in the first album, "The Chase" is an action theme that makes you want to break into a run.
Hats must go off to the Doctor Who Symphonic Spectacular concerts, with the show's music performed by Australian symphony orchestras. Two excellent ones by the Melbourne Symphony Orchestra: "Fifty", a performance of "This is Gallifrey" which segues into Murray Gold's "Song for Fifty", and "The Time of the Doctor", a suite of music from the 2013 Christmas special.