For a while in The '60s, classic comic strip Dick Tracy tried to capitalize on the ongoing Space Race by sending its characters TO THE MOON! One character even got married to a "Moon Maid". After the moon landing, however, the moon and most of the sci-fi elements were dropped from the strip, and Dick Tracy went back to old-fashioned crimefighting...
... then the strip almost immediately stumbled into a second Dork Age with its faux-blaxploitation/"street-wise" 1970s style, including giving Tracy a god-awful mustache and longer hair. And lest you think "god-awful" is putting it too strongly, we should inform you that even in-universe, Tracy's friends hated his mustache so much that they eventually forced him to shave it off.
Both of these periods (which may as well have been a single long one) carry the undercurrent of creator Chester Gould's increasing conservatism. Starting in the early 1960s, Gould would regularly halt the story progression to rant about the Warren Court's decisions on the rights of the accused. Like the more obvious Dork Age mentioned above, these author filibusters would only stop with Gould's retirement in 1977.
The strip would eventually hit a third Dork Age from 2006 to 2011, which is widely considered to be its absolute worst period. A combination of artist Dick Locher's advancing years and the failure to replace writer Mike Kilian after his death led to five years that were marked by atrociously bad artwork and stories that tended to drag on for three or four months without much of anything happening, before everything was suddenly and unsatisfactory wrapped up in just a few days. Fortunately, the strip was able to recover yet again when Locher left and was replaced by Joe Staton and Mike Curtis.
For Better or for Worse is widely considered to have ended on one of these, then restarted on another. It became a soapbox for the creator's very dated (and somewhat warped) views and beliefs. Not helping is the reboot seems to be designed to vilify John (who was based on her ex-husband) as much as possible.
Due to the rather static nature of Garfield, it can be difficult to tell whether the strip is in one or not. The general consensus is that the comic became horribly stagnant starting in the late 1990s – during this period, nearly every single weekday strip consisted of Jon and Garfield at the table and most Sunday strips dealt with the spiders. The base broke when Jon and Liz became a couple (with many fans accusing the comic of jumping the shark), because it destroyed the potential for any future "Jon has a horrible love life and/or has insane wacky dates" jokes – a major theme of the strip.
More infamously, around this same time in the late 1990s, the strip – which actually has quite a large ensemble cast – cut back on the appearances of nearly every side character (Nermal for instance), in favour of just Jon and Garfield with occasional Odie. Later, Liz's increased role led to even Odie only showing up even less occasionally.
True purists of the strip might contend that Garfield entered its greatest Dork Age in the late '80s, when the strip was at the height of its popularity. Maybe it was an attempt to compete with the new breed of zany and/or surreal strips such as Calvin and Hobbes, maybe it was a blatant attempt to appeal to children... but for whatever reason, Garfield descended to pure absurdism. Jon Arbuckle changed from a modestly cool guy to an outright Nerd, Odie went from being merely The Ditz to borderline retarded (and to drooling a lot - seriously, a lot), and Garfield himself unexpectedly transforming from the passive-aggressive Snark Knight he was originally to a certifiable Cloudcuckoolander, wearing banana peels on his head and grinning like an idiot. Of course, this was also during the debut of the Garfield and Friends TV cartoon, so maybe a little zaniness was necessary in order to keep everything consistent.
With B.C., near the end of his life, Johnny Hart became very heavily Christian, and started shoehorning his fundamentalist beliefs into the comic, leading to some controversy (one infamous Sunday strip had a menorah morph into a cross). After Hart's death, his kids took over the strip and changed it back to its original light comedy format.
Funky Winkerbean was simple enough – a wacky comic that took place in a high-school. Years later, after a few in-universe timeskips, it became one of the most dark & depressing comics ever syndicated. Constant mention of cancer, death, characters trapped in a miserable world, and even a story arc of one of the major characters getting cancer and slowly dying from it for the reading public to follow. Even its sister comic Crankshaft (which is in the same continuity) can't escape the constant gloom that all the characters suffer from. This isn't an dramatic exaggeration either; read Funky Winkerbean's trope page.
Doonesbury seemed to hit one in the late-Aughties as Garry Trudeau spent more and more of the strip's time focusing on the Iraq War, eschewing most of the political satire he was known for in favor of observations that were rarely funny. The nadir came when he spent several months on B.D. losing his leg and Alex's boyfriend returning to America after getting brain damage from an IED. Some Anvils Need to Be Dropped, certainly, but Trudeau was not nearly as maudlin with his strip during the Vietnam War.