Here the hamming tradition begun. Thus "theatrical" became a synonym for "very hammy". The extra ham needed for theatre was justified since there were no microphones back then. People in the cheap seats, take the fat off your faces.
Actors and Other Performers
Sarah Bernhardt was the original modern theatre Large Ham, even taking on Large Ham male roles. She was also a Real LifeDeterminator — even being one-legged with almost no mobility could stop her from being an acclaimed actress.
Even in the World of Ham that is Cirque du Soleil, Brian Dewhurst is in a class of his own — an Englishman born into a circus family in 1932, he had a huge list of credits in circus and cabaret long before he made his first Cirque appearance in 1990's Nouvelle Experience as the ostentatious Great Chamberlain. He played a similar role in Fascination, and after several years of behind-the-scenes work let his love of being a large ham lead him back into the limelight as Mystere's principal clown, "Brian Le Petit". He was 68 then; now in his early 80s, he's still in the role, and audiences love him for it. (Cirque being a Silence Is Golden world, he primarily uses his face and body to "project" to the back rows.)
Jesus Christ Superstar can have several parts with lots of ham. Caiphas in "This Jesus Must Die," for one, and Pilate in "Pilate and Christ" and "Trial Before Pilate." Judas is pretty hammy too.
Jesus himself can break out the ham as well, especially Ian Gillan in the original cast version. He screams a fair bit of his lines, and the most remembered part of "Gethsemane" consists of his anguished screams. ("WHYYYYY!? WHYYY SHOULD I DIIIIIIE!?")
A Very Potter Musical contains copious amounts of ham. "Did somebody say Ron? / Draco?", Cho Chang gets a special intro dance, the first scene Voldemort gets with a body, he gets a (literal) song and dance about it, Bellatrix spends her tenure running about, shouting, and getting wet over her dark lord, Umbridge needs to be seen to be believed, and Dumbledore's entrance is ridiculously long note on 'Weeeeeeeeeeeeeeeeeeeeeeeelcoooooooooome'.
Snape's the reason they have such limited scenery, though. Man walks on stage and everyone suddenly feels like they've nommed their way through a Costco-sized pack of bacon.
Practically a requirement for anyone playing Richard Henry Lee in 1776, as the script has him constantly making "Lee"/"-ly" puns on adverbs and proclaiming he will single-handed-Lee deliver Virginia to the independence movement or may he be cursed forever. Lee's involvement in the play amounts to basically two scenes and the original Broadway actor still won a Tony because his musical number performance was just that memorable.
George Hearn's performance as Albin in the original Broadway staging of La Cage aux folles was parodied by Forbidden Broadway as follows: "I ham what I ham/And when I ham, I get ovations..."
Really, Albin — aka Zaza — is a role that demands lovable, heartfelt hamming no matter who's playing him, and those who live up to it are embraced by audiences. A 2008 London revival made its way to the West End and then Broadway — just five years after a 2004 revival in New York proved a disappointment — largely on the strength of Douglas Hodge's performance in the role. His voice isn't as big as Hearn's, but he makes up for it in sheer emotion. (And like Hearn, he won a Tony Award for his performance.)
Maureen in RENT. An offstage character until "Over The Moon", she takes over the show during that number and much of Act 2.
The Engineer in Miss Saigon. The show's dark comic relief, this guy steals the show from right under the main characters' feet if played right.
Large Ham: Now comes in CD form! Pick up a copy of the 2005 Little Women musical and skip ahead to "The Weekly Volcano Press." Words cannot describe the awesomeness of the entire cast (all... seven of them) hamming the life out of a pulpy, Faux Symbolism fairy tale, clearly having far, far too much fun.
The French Ambassador in Of Thee I Sing. "My country, she is deeply hurt. Not since the days of Louis the Seventh, the Eighth, the Ninth, the Tenth, and possibly the Eleventh has such a thing happened!"
This is practically a requirement for the Leonard Bernstein operetta version of Voltaire's Candide. Of special note for the level of salt-cured goodness, however, is Kristin Chenoweth's 2004 turn as Cunegonde, in which she was clearly having a grand old time. See an example.
Basically every single last character in Little Shop of Horrors if the production's any good. It's quicker to list lines that aren't pure ham than that are, provided you can think of any.
No matter how good the actors are in all the rest of the show, just try to find a production of Les Misérables where every confrontation between Valjean and Javert doesn't immediately become a giant scenery-chewing contest. Just try.
The 2013 adaptation of Charlie and the Chocolate Factory is set in a World of Ham — which makes sense, given that in-story there's a lot of scenery that can literally be chewed on — with Charlie and his parents the only characters exempt. But there's no contest as to the biggest ham of all once Willy Wonka reveals himself to the world with the Act One finale "It Must Be Believed to Be Seen", a song that was clearly written for the express purpose of rafter-rattling, and Douglas Hodge is up to that challenge on the cast album.
If you perform A Midsummer Night's Dream and your Nick Bottom is not hammier than all three little pigs, you're doing it wrong. He may be the hammiest ham ever hammed. His lines are specifically written to encourage acting like this, including a bit where he tries to play both of the Show Within a Show's Star-Crossed Lovers. He even claims that he wants a "part to tear a cat in, to make all split". That's Shakespearean for "I want to play a Large Ham."
Sweeney Todd: The Demon Barber of Fleet Street: A musical with melodramatic tendencies and a tip of the blood-spattered hat to the Grand Guignol shows. Mrs. Lovett's infamous meat pies often come with a side of ham. Just how much and for which characters depends on the production, but it's pretty much a given for Pirelli, who just isn't Pirelli if he isn't played as ham with a side of bacon.
The song ''A Little Priest", the Act I finale, is chock-full of ham and lampshades its own hamminess. The movie tried to do it without being hammy and thus demonstrates that ham is sometimes necessary.
Miles Gloriosus in A Funny Thing Happened on the Way to the Forum. Actually, most of the main characters in this require some degree of ham.
Most of the cast of characters in Fools, with special mention to Count Yousekevitch.
Tito Merelli in Lend Me a Tenor is all about the operatic ham.
Other performance forms
Pretty much all of opera. Inevitable when your medium is the narration of every little thing that happens to you via really loud singing. And let's not even get started on any aria and solo parts, and especially the "buffo" role. Romantic operas, even more so.
But for starters one usually whet one's appetite with the Verdi mezzo soprano-contralto roles: Amneris, Eboli, Azucena and Ulrica had been stealing shows since their inception (in case of Amneris & Azucena, the ham is in fact written in the score. One scene for Amneris instructs the singer to exit like a certified crazy person, done very marvellously in this video).
For Murder on Center Stage...there's Stanley the Janitor. In his Shakespearean acting.
The Gilbert and Sullivan operettas require overacting from the entire cast. One Large Ham that manages to stick out due to his flamboyancy is the Pirate King of The Pirates of Penzance, especially in his songs "For I am a Pirate King" and "With Catlike Tread".