Blondie was originally about the adventures of single flapper Blondie Boopadoop, but eventually her suitor Dagwood Bumstead won her hand and became the central character.
Snoopy of Peanuts started out as a minor character and a more ordinary dog.
Pig-Pen was a massively popular character in the strip despite being hated as a one-off joke by Schulz. Schulz was eventually forced to include him occasionally throughout the 60's and 70's.
Mutts began with only Earl the dog and his owner Ozzie. Mooch the cat was supposed to appear for just one arc. Now he has at least as much importance and face time as Earl. As the cartoonist puts it, "You know how cats have a way of taking over the place."
Dilbert has at least two cases in which one-shot characters joined the main cast by popular demand: Ratbert and Catbert. Scott Adams hadn't even named the latter when he got deluged with emails for "more Catbert."
Dogbert once summed up this trope while discussing LOUD HOWARD:
Dogbert: A disturbing number of you have requested the return of Loud Howard. Loud Howard is one-dimensional. There is nothing clever or insightful about him. He is simply loud. It is a mystery why anyone would want more of this guy. Loud Howard: THEY LOVE ME!
Opus, the main character of Bloom County and two other comic strips by Berke Breathed, was originally intended to appear for one week-long arc, but after an enormous amount of fanmail, the author promoted him to a recurring character. Finally, after a huge fan response to one particular◊ Sunday strip featuring Opus, he became the main character of the comic.
Bill the Cat started as a one-shot spoof on Garfield and Garfield merchandising. Ironic considering Bill's later merchandise empire.
Rosalyn the babysitter from Calvin and Hobbes was first created for a single brief story arc, but Bill Watterson surprised himself with her unique ability to completely intimidate Calvin, so several more babysitting stories (and one swimming class story) followed. In her final appearance she even got to literally beat Calvin at his own game and get him to go to bed without any hassle.
A certain strip used to be called Robotman. Then it was Robotman and Monty. Now Robotman's retired and it's just Monty, but there is quite a large cast and entire story arcs are based on other characters.
Mac Manc Mcmanx/M3/M&M&M from Get Fuzzy. Come on, he constantly speaks in confusing British lingo, squats in Rob's house and gets detained at an airport for having a friend named Al Kayda. He's just awesome. Also, there's Chubby Huggs.
Kevin, the "Lost Bunny of the Apocalypse," has practically usurped the position of main character in Prickly City, especially since his 2010 election to the Senate and 2012 Presidential campaign.
Sheila Roo seems to be a fan favorite in Pluggers, most likely for being the furthest from the "old/fat/slob/cheapskate" stereotype displayed by almost all other characters.
Pierce of Zits is so popular as a secondary character that the creators put out Pierced, a compilation of every strip in which he had appeared to that point.