I'm interested in learning more about manga that became popular enough to get adapted into other forms of media (such as anime, live-action, movies, etc.), AND said adaptation having an influence on the original manga.

Example: Detective Conan

This 1994 manga series had a lot of nameless characters that were intended to be one-offs or limited in appearance. From 1996 onwards, some of these characters were given names, which would eventually be used in the manga. A few of these characters even developed into more important roles in the story.

An original character was also made up for the movies. He was intended to be a movie-only character, but he eventually appeared in the TV anime series, and later on, he became an addition to the manga.

It's not enough that a manga has been adapted; the adaptation needs to have changed the course of the original manga in some capacity.

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If I've made a thread in the "I'm Looking For..." forum, I am only interested in Japanese manga. I am not interested in non-Japanese media at this time.

im not too sure about this one but Nurahiyon no Mago. That started off as a one shot but was made into an offical manga.

I remember reading that Trigun Maximum was influenced by its anime. I can't recall where exactly I've seen it, but looking at the chronology it seems fairly believable.
Original Trigun manga: 1995-05 - 1997-02
Trigun Maximum: 1997-12 - 2007-05
Trigun anime: 1998-04 - 1998-09

As for details, the only thing I was able to find right now is this:
"Yasuhiro Nightow loved the anime, largely because it was able to distill so neatly the manga's basic messages. He even drew the anime's filler characters into later manga chapters whenever an opportunity presented itself."
from http://tvtropes.org/pmwiki/pmwiki.php/Trivia/Trigun
(TVTropes is far from what I would call a reliable source, but it's the only one I found after a quick search and it's better than nothing.)

There was a minor bit of this in Akatsuki no Yona. When the manga was adapted into an anime the mangaka went back and gave names to some minor pirates in the green dragon arc and upped the romance quotient based on the response to the anime..

This page might be of interest for you.

It's about characters that first appeared in an adaption of a work only to be "imported" into the original.