Averted with some of the oldest comic strips, which remain impressive and even jaw-dropping after nearly a century (or sometimes even longer) has passed. The stories and their themes are still pretty quirky, and the artwork is often surprisingly good, even excellent. This is partly because the earliest comic strips were regarded as nothing more than a cheap publicity gimmick, so high standards weren't expected of them; this gave the early cartoonists a lot of room for experimentation.
B.C.. When it started in the late 1950s, its use of blatant anachronism was fresh and original. Characters used modern slang and Stone Age equivalents of modern technology, and this was a source of much of the humor. Over the decades this approach became the fallback for comic strips set in the past, which hurt B.C.'s reputation. The strip's legacy became even more obscured by The Eighties, at which point the cartoonist became a born-again Christian and began using the strip as a soapbox for his religious beliefs.
Doonesbury. Many subsequent comic strips have imitated its dry wit. Indirectly if not directly, it had more influence on web comics than anything other than manga.
Doonesbury was the first newspaper comic to regularly have two punchlines in the last panel: a primary joke, and a secondary one which built off the first. It was special at the time. Now almost every comic does it, making those old strips seem run-of-the-mill instead of groundbreaking.
Because geeky web comics like Penny Arcade are omnipresent on the internet today, it's easy to forget how unique "FoxTrot"'s relatively frequent forays into geek and pop culture in the early 90s were, especially in comparison to what was in the funnies at the time.
The Far Side by Gary Larson. The comic strip's format has been imitated so much and so badly over the years that it's kind of hard to appreciate his originals and just how groundbreaking they were.
And controversial as well. The Black Comedy in it that seems extremely tame today? That was extremely uncommon in newspaper comics at the time, and got a lot of bad reactions from the Moral Guardians.
Garfield. Yes, believe it or not, some of the style of the strip was considered risky at the time, and the published books of the series was some of the first to utilize the 'mini-sized' formats that many newspaper comic collections use today. Oh yeah, and quite a few of the strips in the early years were actually controversial and Jim Davis received many complaints for one of the gags he pulled. ("Shake it, Annette," for instance.) A lot of younger people would think you were joking if you told them this fact.
Calvin and Hobbes, too. When it first appeared in newspapers in 1985, it was rare both in comic strips and in popular fiction generally for parents to be portrayed as anything more than slightly exasperated at the antics of their children. Many readers wrote in to complain that Calvin's parents' attitudes toward their son made them mean, perhaps even abusive. Ten years later, creator Bill Watterson could remark with some satisfaction that TV sitcoms with smart-mouthed kids and sarcastic parents had become the norm - and Calvin's parents now looked tolerant and even loving.
Dilbert, not just in Newspaper Comics, but in a wide variety of media, especially live-action TV. Someone unfamiliar with the comics, but a fan of The Office or Office Space might find the similarities close enough to cry plagiarism.
Peanuts was innovative in two ways: Because of the limited space, Charles Schulz had to rely on an ultra-simplistic art style with exaggerated facial expressions. He even developed an emotional shorthand, most famously the "eye parentheses" representing shock. A few decades later, newspapers would run so many comic strips that pretty much everyone had to make their illustrations understandable in the few square inches they received. The second was that Peanuts was one of the darker portrayals of childhood at the time: All of the children in the series were dysfunctional to some degree and fought frequently among each other. Comics like The Family Circus were the main competition during the series's early years, making Peanuts something of a South Park of its time.
For Better or for Worse might look like just another strip starring an angst-ridden mother who's overwhelmed by seemingly endless housework and cursed with an oaf husband and needy children who seem to live in fear of admitting that she's a person too but back in 1979, it was pretty much revolutionary to admit that yes, happy homemakers were anything but content with the rut they found themselves in.