For many decades, Bela Lugosi would have been the actor most associated with the role of Dracula here in the United States. But it’s been more than 90 years since it was originally released, and like most popular entertainers, memory of them fades after death.
No, but he can get confused with Michael Sheen. 
Can’t believe no one has mentioned Johnny Depp!
After he appeared on 22 Jump Street and the original Nightmare on Elm Street he has racked up an impressive list of characters.
Edward Scissorhands
Ed Wood
Sam in Benny and Joon
Gilbert Grape
Captain Jack Sparrow
Don Juan DeMarco
Donnie Brasco
Raoul Duke - Fear and Loathing in Las Vegas
Ichabod Crane
Sweeney Todd
Tonto
Willy Wonka
… and a ton of other weird, eccentric, and historical figures.
Forget it Nars, it’s SDMB-town.
Whose prisoner you are, and from which there is no escape.
The only woman listed here is Elizabeth Taylor but she doesn’t exactly meet the criteria of the OP, which is the same role in multiple movies. She did play the daughter in “Father of the Bride” and “Father’s Little Dividend” but does anyone even remember the name of the character?
Sigourney Weaver’s Ripley would count but Sigourney didn’t have any other roles in franchises. The same goes for Carrie Fisher’s Leia. The iconic roles listed in this thread are for the most part action hero roles, a lot of them taken from literature. There doesn’t seem to be many iconic characters written for women. Or at least considered worthy of filming.
She was in both Avatar movies so far, but in the second one she appeared as Grace Augustine (her character from the original film) only in one or two brief scenes. She also played Grace’s 14-year-old daughter Kiri in the second film, through the magic of CGI. She is slated to play Kiri again in the last two installments.
She was also Dana Barrett in both Ghostbusters and the forgettable Ghostbusters II
Eddie Murphy:
as Reggie Hammond in 48 Hours and Another 48 Hours
as Sherman Klump and six other characters in both The Nutty Professor and The Nutty Professor II: The Klumps
as Prince Akeem Joffer and three other characters in both Coming to America and Coming 2 America
as Axel Foley in Beverley Hills Cop and two sequels
as Donkey in four Shrek films
as Dr. Dolittle in two films
I was going to mention Samuel Jackson, since he has at least three multi-movie characters (Nick Fury, Mace Windu, Darius Kincaid [Hitman’s series]) and plenty of other iconic single movie roles.
But the lack of female iconic characters makes me jump to my second mention, Zoe Saldana!
Uhura (3 reboot movies), Gamora (many MCU), and Neytiri (Avatar)!
And a cameo in Ghostbusters: Afterlife
He’s the one I was going to suggest.
Reeves has nine different action figures; Duke Caboom, Jack Traven, John Constantine, John Wick, Johnny Silverhand, Johnny Utah, Neo, Ted Logan, and himself.
Angelina Jolie: Lara Croft and Maleficient
Wasn’t he also Johnny Mnemonic? Or is that one of the Johnathans you mentioned?
He was, but nobody would call the role or the movie iconic.
You know, in Hollywood productions, we could start talking about how Jackie Chan was Chief Inspector Lee in the RUSH HOUR films, and John Wayne Chon Wang in the SHANGHAI NOON films, and Master Monkey in the KUNG FU PANDA films — but how about Wong Fei Hung in the DRUNKEN MASTER films? Or Jackie in the ARMOUR OF GOD films? The POLICE STORY sequel he did with Michelle Yeoh? The LUCKY STARS sequels he did with Sammo Hung? And so on?
(And I see he’s now Splinter in the new TMNT movie that must be meant to spark a sequel, right?)
Were those iconic characters, or were they all Jackie Chans?
…they were all Jackie Chans, but wearing different pants.
Because one pair of pants isn’t big enough to hold Jackie Chan.
A long, long time ago, I posted a trivia question:
What actor has reprised the most different roles. And even then I believed it was Ford. …wasn’t think of voice actors. There’s a good chance he’ll add Thunderbolt Ross to the list now that he’s replaced William Hurt.
And in Predator! Less Arnie speak…better film.