Played for Laughs and exaggerated in one FoxTrot storyline. In it, Andy is reading about the popularity of Dilbert and its then-upcoming animated counterpart and ponders what the secret to its success is. Each strip for the first five days involved Andy coming up with a new theory, followed by the strip then shamelessly attempting to rip it off. In the end, Andy decides it must be something unique to Dilbert...at which point the comic begins to shamelessly rip off Calvin and Hobbes.
Gary Larson's one-panel comic The Far Side spawned quite a few one-panel gag comics with bizarre humor and no recurring characters, such as Close to Home, Real Life Adventures, Bizarro, and The Argyle Sweater. Mother Goose and Grimm sometimes engages in Far Side-style humor as well.
For the first Garfield compilation, Jim Davis came up with a new long-page book design to accommodate the three-panel strip most legibly. Once the "Garfield format" of books became popular, many other comic strip trade books began using it as well, including FoxTrot and the aforementioned Far Side. (Ironically, Garfield itself no longer does.)
Interestingly, Marvin seems to have aped a lot of the stylistic traits from early Garfield.
Incidentally, Garfield himself is this, debuting five years after another orange fat cat, Heathcliff.
Doonesbury was one of the first comic strips to use a One-Two Punchline, now seen in countless comics. It's also the Trope Maker for every strip that even so much as dabbles in political/topical humor.
And if Doonesbury didn't do it first, chances are the more off-the-wall Bloom County did. Interestingly, Berke Breathed admits that he cribbed Doonesbury a lot in the early years.
Bloom County itself led to a few imitators, including Hartland, Thatch, and Free for All (later a short-lived series on Showtime). Interestingly, only Hartland came out when Bloom County was still in newspapers (and, in fact, ended within few months of each-other); the other two entered syndication after Bloom ended.
The execrable strip Shadows, which ran in The Sun in 2012/2013, was an obvious attempt to cash in on the vampire craze reignited by Twilight. It didn't last very long and was soon replaced by the strip it had itself replaced.
After Peanuts became a hit, more comic strips featuring kids acting like adults started to appear, some of which featured pets not unlike Snoopy. These examples include Small World, Miss Peach, and Winthrop.