Eh, I think that calling an often repeated character / character type a trope is accurate (see 2nd definition sense of “a common or overused theme or device; cliché”):
Not if the writer explicitly bases a character on another one (e.g. as in in the examples @Reno_Nevada_Jr give “lets write Sherlock Holmes as a modern doctor” or “lets write Sherlock Holmes as a medieval monk,”) That’s an allusion or an homage.
But the Moriarity-type super villain is absolutely a trope, and a very widespread one. The “Napoloen of Crime” archetype is pretty much ubiquitous, even though no one is going “Lets write Moriarty as an evil billionaire industrialist”
Although Varney the Vampire may be the first sympathetic vampire in literature, I feel the appearance and brief success of Barnabas Collins in Dark Shadows led to the modern slew of sympathetic vampires.
Hmm…maybe individual reimaginings of the Holmes character are allusion or homage as in those examples, yes, but in general I think the repeated use of a character or character type could be considered a trope. So in other words an individual example could be homage while being part of a larger trope.
But where’s the line between “Sherlock Holmes as ______” and “a ______ who’s a Sherlock Holmes-type of character”?
It the consciousness of the decision. To me a trope is something that has become part of the common language of storytelling, so much so you no longer have to explicitly say “I’m writing this character as Sherlock Holmes in space” you just write a cerebral hero who solves crimes with a side kick using deduction. To keep coming back to Holmes vs Moriaity, there are there fewer examples of that for Holmes than for Moriarity. The “hero has nemesis who is genius super villain” trope is a far bigger part of the language of storytelling.
James Bond is the ultimate trope not only because it spawned many alike characters in the spy genre but also because the tropes themselves got parodied in satire movies of the spy genre. Dean Martin played Matt Helm in four movies I believe that were a ribbing of the Bond image.
Furthermore once the Cold War ended suddenly James Bond had a problem because other spy movies could be written to advance with time but Bond was quintessentially a Cold War establishment gentleman killer spy all in one go. The smoke and mirrors of those kind of spy days was finished. This led to what Pierce Brosnan has subsequently reasoned a period of reflection where the demand was still really high to pump out Bond but the franchise weren’t sure which way to go so while his movies did well at the time retrospectively they don’t rank as high in public surveys because they come across generic action thrillers. He did several movies that had a bit of everything that came before him but nothing stand out. Daniel Craig in a post 9/11 surveillance world had the franchise embrace bringing Bond into modernity and which meant changing the tropes around somewhat.
See also: James Coburn’s outings as superspy Derek Flint (complete with a running gag about British agent Triple-0-8).
Maybe “stock character” is more accurate?
Actually, I came to this thread to post Conan as a character that became the trope of the barbarian hero. 
Not that we wouldn’t have overlap with various ‘noble savage’ characters, such as Tarzan which have been previously mentioned. As for Elric, I always felt his character was a clear descendant of the various doomed/geased Celtic heroes. Similar themes are seen in Arthurian myth (which drew from many of the same Celtic sources in part).
Apparently Moorcock drew upon more contemporary sources for his inspirations for Elric, at least according to articles I read in the past, but they in turn drew on yet older sources. For that matter, I’m sure that self dooming heroes are a truly ancient trope, since they’re ubiquitous in Greek myth.
Well, my OP was about actual characters who are reused and reimagined so often they become tropes (whether ‘trope’ is the accurate term for that aside), either as the actual character or as a thinly disguised knockoff. That Wikipedia list of stock characters is an interesting read, but are more generic than my original meaning in creating the OP. But thanks for the article, I like reading stuff like that.
There’s the biblical story of Moses…
Harry Potter might as well be the cover art for modern printings of Hero With A Thousand Faces
My first thought when reading the thread title was Falstaff.
Dennis Hopper’s wigged-out photojournalist character in Apocalypse Now. Not sure how many of you will agree, but I think I see a lot of actors channeling that performance when they portray an “insider” who appears to be a potential accomplice or at least potentially sympathetic to the protagonist’s cause but turns out to be bat-shit crazy.
Maybe Hopper was channeling someone else’s interpretation of the Renfield character in Dracula.
The only thing Hopper was likely channeling was cocaine directly into his nose 
The character of Arsène Lupin as the “gentleman criminal”. Has appeared in various forms and media since 1905 (including the classic anime Lupin III and a Netflix film Lupin) and likely the mold for such characters as Thomas Crown, Danny Ocean and his gang, Simon “The Saint” Templar, any number of characters from Guy Richie films and various other imitators.
As I pointed out already, A.J. Raffles was the originator of the trope, predating Lupin by seven years
Yep. See that now. 
Someone mentioned Bond way back near the beginning of the thread. As I read that, I realized that I couldn’t think of any Bond-character who wasn’t a parody. Or at least started out as such, even if they may have become serious later. Certainly Flint and Helm were parodies. Napoleon Solo (Man from UNCLE) started off that way. And of course Austin Powers.
Now there are probably some that weren’t parodies, and I’m sure everyone will have fun letting me know about them.
I’m trying to think of what set Bond apart from previous fictional spies. I think maybe it’s that he was the first male spy to incorporate Mata Hari type romancing techniques into his craft.