Start off conventional, end up weird

Well, once they’d explored Heaven, Hell, and Purgatory, and the brothers had to literally avert the Apocalypse, they didn’t leave themselves a lot of areas to explore.

The real “jump the shark” moment though, in my opinion, was when they meet God… and he’s basically writing fan fiction about them.

Bob Dylan started out as a typical early 1960’s folk singer when folk music was the most popular music of the time.

His getting the Nobel Prize for Poetry was extremely, jaw dropping, unbelievably are you fucking kidding me? WEIRD.

I’m kinda surprised Twin Peaks hasn’t been mentioned yet. That seems to be the ultimate example IMO. Of course, that show stated off a bit weird, but still was more-or-less conventional (if convoluted) for the first few episodes. The second season is when it went nuts.

Speaking of Peanuts, in the beginning Snoopy was a conventional dog. Period.

In the end, he was a very very very very very weird dog.

I think that what might be the poster child for this is Chester Gould’s strip Dick Tracy. Although the gritty police strip did have its moments of weirdness (like Tracy’s iconic Two-Way-Wrist Radio*, which was well ahead of its time), it’s weirdness was mainly concentrated in his oddball Rogue’s Gallery, with their defining physical characteristics.

But in the 1960s, the strip took a turn for the Truly Weird, with the police getting the Space Coupe and meeting intelligent folks from the moon, with antennas and all, including Moon Maid:

Out of the Dark by David Weber definitely qualifies. It starts out as a military sci fi novel… aliens invade earth, they have more advanced technology, but humans (particularly Americans, of course) are purer of heart and spirit, and do their best to hold off the aliens, with American military tech described at nearly-pornographic length.

But… the aliens are just too advanced, and they’re going to win, until humanity is saved by…

…introduced reasonably late in the book with basically no foreshadowing…

Dracula.

They didn’t go full weird, but Maverick was originally one of many standard westerns in a sea of standard westerns. But one day, some writer put stage directions about Maverick looking at someone “with his beady little eyes” and Garner thought it was hilarious. From then on, Maverick was much more a comedy, and a legend was born.

NewsRadio is another example of a sitcom that got weirder (in a good way) as it went along.

Dylan didn’t change. The world did.

As mentioned in both the wikipedia and Dick Tracy Wiki articles you link to, the current creative team, Joe Staton and Mike Curtis, have reintroduced a lot of older elements from the classic Tracy strips, including some of the moon-related material. Honeymoon Tracy, complete with antennae, has become a more prominent character again. And as recently as the October 18 strip, a space coupe carrying what is apparently a visitor from the moon has landed on earth. Nothing further has come of this plotline yet, but it looks like they’re gearing up for a genuine Moon Period-style adventure.

After the first new team first killed off the whole story line off when they took over the strip. It looks as if history may be repeating itself – looking for more interest, the current team is going from “conventional” (well, Dick Tracy Conventional) to Weird again.

You know, It’s Always Sunny started off pretty normal and went real far off the rails soon after. In the first couple episodes, Charlie isn’t retarded. I think once Frank came along, all bets were off. That last season was damn near unwatchable.