I'm taking Sherlock Holmes as my example here, since I just watched another episode of the new "Sherlock" series (which is a FANTASTIC adaptation, that's maybe the best updating of any literary work into the modern day ever, almost everything that makes the characters who they are is intact, and almost none of the updates take away from the spirit of the old stories) and I have Holmes on my mind again, he and Hamlet being my favorite characters far and away, the ones (to use the dreaded term) I can "relate" to the most on a level.
The first Holmes story I ever read, I still remember, was "The Solitary Cyclist."
I won't spoil it in case you've never read it--in which case, either go ahead and read it, it's really not long, it's one of the 56 short stories, or else YouTube the story and you should find the whole thing via the Jeremy Brett version, which is THE version of traditional Sherlock Holmes, I'd argue, for adaptation...Basil Rathbone's movie versions are classic, but a lot of them are their own stories and not originals...in any case, Brett and Rathbone are probably the two most famous and associated Holmes in film and TV, but I digress--but it's very much your typical Holmes story, full of him deducing and a fortune as well as lives at stake and advances and mistakes being made along the way...
And I personally really like the ending...which again, I won't spoil.
Conan Doyle never considered it one of his best ones, and there ARE far better ones, but that one will always be special to me as it was the first one I read as a kid and the first introduction I got to Sherlock Holmes and Dr. Watson...
And I think Conan Doyle sold the story a bit short, actually--it is a good Holmes story, that it's no The Final Problem/The Empty House double-part epic spaced years apart or something as famous as A Scandal in Bohemia (which the "Sherlock" adaptation did reasonably well, though I think their take on Irene Adler ultimately made her a bit weaker than what she was in the original story by trying to over-sexualize her rather than sell her for what she was in the story, a beautiful woman with a sharp mind, the combination of which take Holmes off guard and allow her to best him for a good part of the story) is no detriment to the story itself.