Doctor Who, in all its myriad incarnations, is a bountiful supply of ham. It's one of the things that makes the series so fun.
In general, the Doctors can ham it up. Of course, depending on the situation, this can either be good or bad for those who cross them.
This especially fits Tom Baker, who hams it up to almost BRIAN BLESSED levels both in the show and off it. Apparently there's a gene in any person with the surname Baker that transforms them into concentrated ham when in the presence of a TARDIS.
"The Mark of the Rani" is one big three-way Ham-fest between Baker ("DON'T MOVE, PERI! THE TREE WON'T HURT YOU!"), Anthony Ainley as the Master ("SHE'LL HAVE A SEIZURE!"), and Kate O'Mara as the Rani ("AND SO WILL ANYONE ELSE WHO INTERFERES!").
Good rule of thumb: the more Time Lords in a story, the bigger your serving of ham.
The exchanges between the Doctor and Yrcanos in "Mindwarp" are great. It's like the Doctor can't decide whether to be annoyed at how loud and over the top Yrcanos is or about him being more over the top than the Doctor himself.
Though his non-hammy evil turn in "The Natural History of Fear" is such concentrated terror that ham would almost be preferable. Hammy evil Eight is entertaining as hell, but his subdued evil manages to be utterly terrifying. (And a bit of Fetish Fuel as well.) Listening to him whisper while he's lobotomizing a woman who's awake, aware, and terrified... good grief.
"You may think the worst thing I can do to you is hurt you..."
Though overall more subtle than Four, Six, and Ten, Christopher Eccleston's Ninth Doctor made ham sandwiches in some episodes.
There was his scene alone with the Dalek in "Dalek", in which Eccleston was literally foaming at the mouth by the end of his scary, awesome speech:
"Why don't you finish the job, and make the Daleks extinct? Rid the universe of your filth! Why don't you just DIE?!"
Pretty much any line from the episode "The Christmas Invasion".
"This hand? It's a fightin' hand!"
And in "The Doctor's Daughter", what could be the hammiest proclamation of pacifism, ever:
"WHEN YOU START THIS NEW WORLD! THIS WORLD OF HUMAN AND HATH! REMEMBER THAT! MAKE THE FOUNDATION OF THIS SOCIETY A MAN WHO NEVER WOULD!"
Since "The Waters of Mars" was one of his last performances as the Doctor, Tennant apparently decided to go out with a bang. The scenery-chewing when he decides to actually take action is so completely over the top it threatens to implode in a singularity of ham.
Tennant manages to compress a metric ton of Ham into one word in "The End of Time": SHIIIIMMER!
The Doctor: "There's an old Earth saying, Captain. A phrase of great power and wisdom, and consolation to the soul in times of need."
Vinvocci: "And what's that then?"
The Doctor: "ALLONNNNS-Y!!" *slams the throttle forward full-blast*
Tennant's most hammy habit was adding explosive "-a!" sounds to the end of words as he got excited and started-a to over-enunciate-a. See "AND I'M NOT LISTENING-A!" from series two's "The Idiot's Lantern" and "BAREFOOT ON THE MOON-A!" from series three's "Smith and Jones" for particularly jarring examples.
Matt Smith is a very talented ham. In keeping with his incarnation's rather self-aware nature, a lot of his hammy moments are also intentional ploys to psych up himself, psych out his enemies, encourage his companions, or all three.
He's quite a ham just after his regeneration:
"Legs! I've still got legs. Good. Arms! Hands! Oooh fingers, lots of fingers! ... Hair? I'm a GIRL?!?"
"The Rings Of Akhaten" has the hammiest Eleven speech yet, complete with Manly Tears:
"I walked away from the Last Great Time War. I marked the passing of the Time Lords. I saw the birth of the universe and I watched as time ran out, moment by moment, until nothing remained. No time. No space. Just me! I've walked in universes where the laws of physics were devised by the mind of a MAD... MAN. I've watched universes freeze and creations burn. I have seen things you wouldn’t believe. I have lost things you'll never understand! And I know things. Secrets that must never be told. Knowledge that must never be spoken. Knowledge that will make parasite gods BLAZE!SO COME OOOOON THEN! TAKE IT! TAKE IT ALL, BABY! HAVE IT! YOU HAVE IT ALL!"
"Nightmare In Silver" had Matt Smith at about thrice the usual ham level, when possessed by the Cyberplanner.
He reaches Brian Blessed levels in "The Time of the Doctor":
Eleventh Doctor: IF YOU WANT MY LIFE, COME...AND...GET IIIIIIIIIIIIIIIIITTTTTTTT!!!
Not to be outdone by his arch-nemesis, The Master is always a prime source of Ham.
Anthony Ainley on playing the Master: "I'm not a ham. You can cure a ham!"
Speaking of The Master, Peri parodies this trope with him:
The Master: I am the Master! Peri: So what? I'm Perpugilliam Brown, and I can shout just as loud as you!
The Master: Ya CRAVEN-'Earteeeed... SPINE-less... POLTROON!
Derek Jacobi during the last ten minutes of his performance in the episode "Utopia". Having given a subtle, moving performance as the kindly Professor Yana for most of the episode, he then is transformed into the Doctor's uber-evil arch-foe the Master... and at the same moment, into a really Large Ham.
John Simm's Master may be the hammiest yet. Four words. "Here! Come! The Drums!"
*cue 'Voodoo Child' by Rogue Traders*
Not to mention that the first minutes of "Last of the Time Lords" (the episode that follows that whole Here Come The Drums thing) is the Master singing "I Can't Decide" by Scissor Sisters.
Davros fits this trope like a glove. He starts out quietly, speaking with precision as he lays out what is about to happen, but he can't contain himself forever and by the end he's shaking with passion and screaming at the top of his voice.
The longer Nicholas Briggs plays the Daleks, the more they're becoming DAAAAAAAAAAHHHHRRRR-LEKS. This is doubly true for every Big Finish episode he wrote himself. (Oh, and he hammily played the Doctor for four seasons in his Doctor Who Audio Visuals.)
Special mention for Andrew as Crassostrea in the Big Finish story "Orbis", who vividly describes how he has to gorge on food and develop female organs so he can SPAAAAWWWN. He then proceeds to invade a nation of jellyfish and give birth, in a glorious explosion of ham.
The Empress of Racnoss, villain of the 2006 Christmas special "The Runaway Bride", was an enormous piece of Spider-Ham. "KIIIIILL THIS LITTLE CHATTERING DOCTOR-MAN!"
To go a little more old school, Professor Zaroff in the Second Doctor story "The Underwater Menace" is a GLORIOUS bit of ham all the way through, his most magnificent bit of ham being the cliffhanger of part three: "NOSSING IN ZE VORLD CAN SHTOP ME NOW!"
The fantastic antics of Graham Crowden in "The Horns of Nimon", particularly his death scene, complete with manic cackling, staring eyes, "Lord Nimon? Lord Niiiiimon? It is I, Soldeed!" and "You Fools! Fools!! You will die for your interference!!!"
Graham Crowden was originally cast as the Fourth Doctor, but turned the part down. Let that sink in for a minute.
Malcolm Terris as the co-pilot was visibly having the most fun of his life. At one point, he overacts so hard that his trousers split. And he gets to face off against Soldeed!
This line was not only improvised on the spot, it was so grand that it got included in the first Big Finish episode featuring the Nimons.
In "The Daleks' Master Plan", Kevin Stoney is both nuanced and over-the-top at the same time, playing the traitorous "I, MAVIC Chen, GUARdian of the Solar System!"
The Captain of "The Pirate Planet" was the biggest ham imaginable (and clearly intentional, with Douglas Adams writing the script), often loudly exclaiming such things as "BY THE BURSTING SUNS OF BANTAR!" and "NO, BY THE SKY DEMON - I SAY NOOO!", but it turned out to be a case of Obfuscating Stupidity — he was actually an engineering genius and trying to hide it.
Other notable quotes of his include:
By the LEFT Frontal LOBE of the SKY DEEEMOOON!
MOOOOOOOOOOONS OF MADNESS!
And when he faces off against the Doctor... well. It's Tom Baker. Put your fingers in your ears.
The K-1 in "Robot" provides some nice moments of Robo-Ham: "AHHHHHH, I HAVE KILLED THE ONE WHO CREATED MEEEEEE!"
Michael Jayston in his role as the Valeyard also fits here wonderfully. He spits out lines like "You cannot speak as though reality is a one-dimensional concept." with such delight in his role. To top it off, his first appearance was 14 episodes long.
The Carrionites in "The Shakespeare Code". Around 1:19.
Rosanna Calvieri of "The Vampires of Venice". Manages to alternate between hamminess and seriousness with ease.
Lady Cassandra. MOISTURIZE ME! (Keeps the Ham nice and juicy.) Also bleeds over into Billie Piper ("It's like living in a bouncy castle!!") and David Tennant ("a little bit fox-ay!") when the Doctor and Rose end up hosting Cassandra's personality.
Aris from "Kinda", when he gets taken over by the Mara and is granted the gift of speech (and Ham).
Aris: I still control them! I am Aris! I. HAVE. VOICE!
Fifth Doctor: YES, SO I HEAR!
The final form of Eldrad, despite only being in one episode, easily produces enough ham to feed a family for months.
Eldrad: I CREATED THIS WOOOOOORRRRRRLLLLLLD!!!!!! IT IS MIIIINE!!! MINE BY RIIIGGGHHHT!!!
Also Omega, from "The Three Doctors", with the help of some truly hammy scriptwriting.
Omega:I created this world through the power of my WILL. I created the organisms which BROUGHT you here. THIS! is the source of the light-stream you travelled along. AND I CREATED IT. I ALONE!!!!! OMEGAAAAAAAAAAAAAAA!!!!!!!
And another example:
The Third Doctor: All my life I've known of you and honoured you as our greatest hero!
Raggedy man, I remember you, andYOU ARE LATE FOR MY WEDDING-A!
River Song. While Alex Kingston tends to be a little more kosher than most Who actors, she appears to be having a little more fun with the character.
"It's like I told you on the dance floor... You might want to find something to hang onto."
"Let's Kill Hitler" features River at her hammiest, because Evil Is Hammy!
Donna Noble, fastest HAM in Chiswick.
Her time as the DoctorDonna transformed Donna into one of the best examples of a female Large Ham, resulting in a bit of Ham-to-Ham Combat between her and David Tennant and a truly amazing David Tennant impersonation. It would have been truly awesome if not for how it ended.
Son Of Mine, from "Human Nature" / "The Family of Blood". Considering his other modes of speaking are Creepy Monotone and Goddamn Unsettling Sing-Song, this is one of the few times where straight up hamming comes as a relief.
The Wire, from the episode "The Idiot's Lantern", really rates a mention here.
Between his wardrobe, mannerisms and obsession with fine dining, one-off villain Shockeye from "The Two Doctors" is one of the hammiest characters ever to appear.
"YOU CANNOT ESCAPE SHOCKEYE O' THE QUANCING GRIG!"
In the 1980s, the Cyber Leader, despite being supposedly emotionless, delivers some of the hammiest lines in the history of the show.
"DESTROY THEM! DESTROY THEM AT ONCE!"
"My army awaits, DOCTOR!"
Sutekh in "Pyramids of Mars" and the Faction Paradox audio series manages to be a Large Ham while speaking in barely more than a whisper. This was lampooned in the DVD extra "Oh Mummy!", in which Sutekh (still voiced by Gabriel Woolfe) attempts to find work after "Pyramids of Mars", featuring a truly unforgettable gag in which Sutekh shows the "documentary" crew his cute little bunnyrabbit. "I call him Neil. Neil. NEIL BEFORE THE MIGHT OF SUTEKH!"
‘Big part, is it?’ ‘Biggest.’ ‘Meaty?’ ‘Bratwurst.’ ‘Does it involve –’ ‘Shouting?’ said his agent. ‘Lots of it. Nothing but. It’s shouting, shouting, shouting. Shouting till the Dryrths come home.’ Prubert swung his chair round. ‘Tell me more.’