He’s played Han Solo, Indiana Jones, Jack Ryan, Rick Deckard and probably a few others that don’t immediately come to mind. Can any other actor match his career for iconic characters?
I don’t have a firm definition for “iconic” but to me, it’s a famous role that has appeared in more than one film.
That’s going to be the tricky part. I can think of actors who’ve played some great characters, but which haven’t spanned multiple films.
With that stipulation in mind, how about Mel Blanc?
There are actors, like John Wayne, who can only play themselves. Harrison Ford is another one. He has no acting range and can only play himself, or the one character he is percived to be.
From Han Solo to Indiana Jones, to Witness to The Fugitive, Blade Runner, all the same guy. And we all love that guy but he is still Bob Falfa from American Grafitti and always will be.
I think Deckard would still be considered iconic (and was for years, I’d argue) even without appearing in BR 2049.
Mel Blanc’s a good one, and on that same sort of idea Billy West jumps to mind: he’s also done a ton of Looney Tunes characters (Bugs, Elmer Fudd, others), Philip J Fry/Farnsworth/Zapp Brannigan, Doug Funnie, Ren and Stimpy, Shaggy Rogers at least once, Woody Woodpecker, Tom (Tom & Jerry)…that’s a pretty good list. EDIT: oh, and the red M&M 
Robert Downey Junior is both Iron Man and Sherlock Holmes
If the Man With No Name counts as a character, then Clint Eastwood is both him and Harry Callahan.
Mel Gibson, God help us, is both Max and Martin Riggs.
And of course, Keanu Reeves is Theodore “Ted” Logan, Neo and John Wick.
Colin Firth
It doesn’t fit your definition for iconic, but might we consider Humphrey Bogart’s various anti-hero roles? Sam Spade, Rick Blaine, Philip Marlowe, Frank McLoud, Fred C. Dobbs, even, to start?
Mike Myers was:
Wayne Campbell
Austin Powers
Dr. Evil
Shrek
At least no director has tried to stick Harrison Ford in a movie as Genghis Khan, so he has that going for him.
Peter Cushing played Tarkin, Sherlock Holmes, and in 90% of the Hammer Horror films
Burt Reynolds was Bandit and JJ McClure (Cannonball Run) but for the most part he played the same character in all his movies.
Basil Rathbone also played Holmes, the Sheriff Of Nottingham (across from Errol Flynn, no less), and a number of movie heavies, including, I believe Dracula. And also Van Helsing, if memory serves. Different films, of course.
Also that OTHER Mr. Darcy, in Pride and Prejudice.
Jason Statham
Again, pretty interchangeable characters. And I’m not sure I’d call any of them iconic.
Michael Caine may not have reprised roles for a bunch of sequels but the guy was in a ton of movies (like 160 or more) and just through the sheer volume of his work managed to score a bunch of memorable roles along the way. Here’s a list someone compiled of his top 50 roles. I easily recall him from at least a dozen of them.
Different times, different ages, different preferences, but…
Mickey Rooney
Santa Claus (various Rankin-Bass productions)
Gus (Night at the Museum franchise)
Andy Hardy (Mickey was THE box office draw of the 1930s)
Mickey McGuire (star of various shorts)
Oswald the Lucky Rabbit (Oswald’s voice)
Himself (any number of movies and TV appearances)
Honorable mention to Dan Aykroyd
Elwood Blues
Ray Stantz
Sylvester Stallone
Certainly the first two are iconic.
He was the first person I thought of, but I don’t know if any of them spanned multiple films. And you left out Philip Francis Queeg.
John Cleese was