The king of hams is Captain Kirk himself. He's pretty much the biggest ham in the galaxy, notably as Captain James Tiberius Kirk. Most famously... he often... talked like... this... while making... strange... hand gestures. And he's only gotten hammier as he's aged.
And then read the number of comments that bring that point up and take it too seriously.
Trelane, the Squire of Gothos. Childishness and enthusiasm are just who he is.
Evil!Sulu is another delicious slice of ham. In fact, most Mirror Universe episodes seem to be an excuse to break out the pork-based products.
In her short acting career, Alice Rawlings got to overact opposite William Shatner. She played a young girl who blamed Kirk for her father's (supposed) death and expressed it in her own subtle way: "YOU MURDERER!!! YOU MURDERER!!!"
A Klingon (the old-school type) in The Trouble with Tribbles says the Enterprise should be hauled away AS garbage (complete with Evil Laugh) in a way so hammy that it's worth a watch even if you have no audio.
It is Michael Pataki, after all.
Commodore Matthew Decker, in command of the U.S.S. Constellation in the episode "The Doomsday Machine", comes across as hammier than Captain Kirk, if such a thing is possible.
Kirk: "Where's your crew?"
Decker: "On the third planet."
Kirk: "There is no third planet!"
Decker: "Don't you think I know that?!! There was!!! But not 'nymore!!!!! They called me!! They BEGGED me for help! Four hundred of them! I couldn't! I, I couldn't!! (begins sobbing)"
LORD!!Garth of Izar. He manages to make Kirk, at his hammiest, look subdued, getting lines like "RRRREMOOOOOVE THIS ANIMAL!!!"
Khan Noonien Singh. Opposite Kirk, the volume in The Wrath of Khan only comes down for the sole purpose of going up again.
Chekov: You lie! On Ceti Alpha V, there was life! A fair chan— Khan: THIS IS CETI ALPHA FIVE!!!!
Lazarus from "The Alternative Factor": "Come! Come! It'll do you no good! I'll chase you to the very fires ofHELL!!!!"
Lenore from "The Conscience Of The King", especially near the ending. Helps that she is part of a troupe of Shakespearean actors.
Gary Mitchell from "Where No Man Has Gone Before". As his psychic powers grew, so did his hamminess.
Any character who's about to pull a Face Heel Turn or suffer some sort of breakdown will act like a Large Ham.
Even though he usually plays a relative Straight Man compared with Kirk and Sisko, Patrick Stewart as Jean-Luc Picard had a couple of truly delicious scenes. "THERE! ARE! FOUR!! LIGHTS!!!" He does, however, ham it up without mercy on the holodeck as Dixon Hill. His horrific Humphrey Bogart impression is hysterical.
And Dukat himself? A prime cut of Cardassian ham, and it gets better as hegetsnuttier:
Dukat: "I'm so glad we had this time together, Benjamin. Because we won't be seeing each other for a while. I have unfinished business on Bajor! They thought I was their enemy! They don't know what it is to be my enemy, but they will!! From this day forward, Bajor is dead. All of Bajor!!! And this time, even their Emissary won't be able to save them!!"
Speaking of Cardassians, Star Trek: Deep Space Nine (specifically, the episode Duet)was the series that introduced us to the so-called "Long Cardassian Monologue", a tendency of Cardassians to go on long hamtacular rants about various and sundry things. That's right. The Cardy's are so hammy that hamminess is encoded right into their genes.
"Our Man Bashir"... Tranporter accident Excuse Plot traps the DS9 staff in Bashir's holodeck program;
Nana Visitor with a wonderfully horrible Russian accent coming out of a wall on a rotating bed.
Avery Brooks again in an early season 1 episode where the crew is driven insane by whacky alien tech "A CLOCK!!!".
The episode in which Nana Visitor (aka Major Kira) plays a holodeck version of a Bond Girl expy essentially consists of Visitor rolling about in a field of ham-nip, utterly glorying in her patently ridiculous Lzherusskie accent and basically playing the character to the hilt. She shamelessly loved every minute.
Steven Berkoff hammed it up shamelessly in his guest roll of Hagath the weapons dealer in the season five episode "Business as Usual". Who could forget his pop-eyed, snarling delivery of lines like "instead of doing your JOB, you were off enjoying yourself" and "Like this? He's going to like THIS??".
With Ferengi society facing complete reform toward the end of the series, Quark's so determined to keep to the old Ferengi ways that he channels Picard from First Contact.
Quark: "I won't preside over the demise of Ferengi civilization! ... The line has to be drawn HERE! THIS FAR, AND NO FARTHER!"
Every character in The Adventures of Captain Proton! hams it up mercilessly, most notably Mad Scientist Doctor Chaotica, Ruler of the Cosmos ("FOOOOOOOOOLLLLLLLLL! You will PAY for your inCOMpetence!"). This is hardly surprising as the holoprogram is based on Republic movie serials like Flash Gordon and Commando Cody. Even crewmembers who initially regard the program with bemused contempt end up playing their roles with gusto — such as the Doctor as The President of Earth, and Captain Janeway as Queen Arachnia of the Spider People.
Chaotica: (dramatic music playing) Full power to the Death Ray!
Kate Mulgrew has said that the king of hams William Shatner was the inspiration for her Queen Arachnia.
Seven of Nine is pretty much an anti-ham, except when she's also the EMH, who must have had hamminess written into his code, or when she's manifesting the personalities of certain assimilated individuals.
The episode that started with the Holographic Doctor putting on an opera in a Dream Sequence, wherein he single handedly saved the crew with his deft hands and his Tenoric rendition of "La Donna e Mobile" ("Tu-vok I un-der-stand / You are a Vul-can man / You have just gone with-out / For sev-en years (about)")
Andy Dick as the Starship Prometheus' EMH Mark-2 was a spazzy slice of Camp Gay holo-Ham.
"My brilliant existence cut short... No time to explore the universe... No time to smell the roses... No time for... sex..."
The Fear Clown from the episode "The Thaw" is a wonderfully hammy bit of total horror.