For many Simpsons characters, one notable trait often comes to define and dominate their existence over time. Coining the term "Flanderization" (for reasons that will be made obvious), it essentially describes the devolution of a character into a caricature. Some Simpsons characters have maintained some level of complexity, but more than a handful suffered this effect and changed so drastically that they became unrecognizable when compared to their original incarnations.
Interestingly, The Simpsons has been going so long that many characters have changed more than once, first finding their iconic molds after a few seasons, then again later as their characters were wrung out and stretched to find the last few gags possible. These are the characters that would be totally unrecognizable when compared to their roots - if you had to describe them without visual aid, anyway.
Waylon Smithers
Skipping right over the fact that early on Smithers was depicted as having dark skin only to change to yellow later, Mr. Burns' right-hand man has morphed insanely over the years. Early on he was a stern, scrupulous cog in the power plant's hierarchy. This meant he was fiercely loyal to his boss, Mr. Burns.
That last fact soon became his defining one, turning to actual love, then utter obsession with his boss, which the show's creators described as his 'Burnsexual' nature. Finally, this attraction became an unambiguous homosexuality, shifting into whatever flavor a gag needed in order to exist.
Moe Szyslak
Early on, Moe was the stereotypical bartender, surly, oily, and sleazy. He raged at the drop of a hat and gave terrible advice to his barflies. He also spent a lot of time being Bart's target for prank calls, coming up with interesting and unique threats in response to Bart's cackling triumph. He also dabbled in illegal schemes, including smuggling whales and pandas.
Now, Moe is the show's depressed and dismal sad sack. Finding new ways and reasons to try to off himself every episode, he seems unable to get through a scene without looking for a place to sling a noose. Moe-bid in the extreme.
Ned Flanders
Given that we've mentioned the eponymous 'Flanderization' effect, it should be obvious where this is going. In the beginning, Ned Flanders was the ideal neighbor to contrast Homer's bumbling, grumbling efforts, with his 'perfect family' shining a glaring light on The Simpsons' shortcomings. This included being faithful, religious churchgoers among many other things, but not for long.
A few seasons in Ned's religiosity dominated his actions and were the butt of plenty of jokes. As the show continued and Ned revealed more stereotyped tendencies, he strayed further and further from his old persona. The ideal man he began as has either been completely changed or has been revealed to be a fraud at this point. His beatnik upbringing left deep-seated mental hurdles that left his facade ready to crumble at a moment's notice.
Principal Seymour Skinner
Famously, Principal Skinner has an episode so divisive concerning changes to his character that fans cite it as the exact moment The Simpsons began spiraling. Beginning simply as an authoritarian principal at Bart and Lisa's school, he has ranged all over the place since. He is somehow a former rebel, but also a Norman Bates-esque son to Agnes Skinner.
He has been so many things at different times, perhaps more than anyone else on the show, and when he was revealed to not even be Seymour Skinner at all, it finally went too far for some fans. But we don't want to fall under 'penalty of torture' so we won't mention Almond Tasmanian, or whatever that identity was.
Homer Simpson
The patriarch of the titular family, Homer has devolved as if at some point he had a crayon shoved into his brain. Originally a 'Walter Matheau' type, Homer quickly got dumber and dumber to the point of genuine concern. The love for his family that always brought him back from the edge is long gone.
Now he's more likely to destroy Springfield than he is to give his kids a lift to their after-school activities. The show now has to 'hang a lampshade' on his wild misadventures just to maintain the last shred of plausibility that the family unit can survive. He's still probably the funniest character but he's unrecognizable from the guy who let Bart take Santa's Little Helper home.
The Wiggum Boys, Ralph & Clancy
Ralph and the Chief were functional members of Springfield Elementary and the police force, respectively, in the beginning. Chief Clancy had a slice of corruption and Ralph never was quite right, but both could still be recognized as functional members of society. Now, that's impossible to say.
Ralph has a single-digit IQ and Chief Wiggum actively helps criminals by sheer force of idiocy. Ralph, in particular, has none of the heart or simple charm that characterized his first appearances. The meme about 'the moment his heart breaks' is more accurately the moment his character lost his last brain cell.
Doctor Julius Hibbert
While the good doctor's laugh has endured, his medical skills have become a joke. In early seasons he was a reliable practitioner, giving sound advice and looking out for the lives of his patients. His counterpart, Dr. Nick, held down the 'medical malpractice' fort.
Nowadays though, Nick has largely disappeared due to a case of terminal death, and Dr. Hibbert has scooped up his mantle. Dr. Hibbert is closer to Family Guy's Dr. Hartman now, declaring without diagnosing and prescribing without prognosis. His laugh could signal a death knell and be pretty on point.
Otto Mann
A kid-friendly hippie who gave the kids a ride to school and wasn't "too cool" to treat them with a little respect. Otto has ratcheted up the reckless drug use, become defined by his musical taste, and is mostly seen wandering into other jokes as a living punchline these days.
The lovable bus driver we knew is long gone. At this point, he's more-or-less a homeless drug addict, since he's more than once tried to live with the titular Simpsons or failed to buy their place because it had 'expensive windows.' A latter season episode showed him thinking he'd accidentally killed almost two-dozen students, and that may explain his descent.
Nelson Muntz
Nelson wasn't markedly different from the other Springfield bullies in the early times, but that has certainly changed. Originally just like Jimbo, Kearney, and Dolph in beating up kids for money and being generally mean, more often than not he's crying over his dad these days.
He's been shown to have decent depth, having dated Lisa, been very progressive even compared to her on some matters, shown vulnerability, and "done quite well in Home Ec." Weirdly, Nelson could by now be the most sympathetic character on the show. Even his trademark 'Haw Haw' has acquired layers of nuance and subtlety through inflections and delivery. A rare upward trajectory for this Springfieldian.
Lisa Simpson
It may seem strange, but very early on Lisa was mostly a sidekick to Bart's prankish ways more than the learned bookworm we know so well. Joining Bart in most efforts to cause a little havoc, she soon changed and was subject to significant character development. From her McCartney-enforced vegetarianism to her spiritual awakening and conversion to Buddhism, Lisa has gone through a lot of phases.
Sure, she's still mostly lecturing and ethically judging the rest of the town, but it's backed up by fundamental core changes that stuck. She may be a bit insufferable at times, but it's hard to argue that she hasn't come along and shifted by leaps and bounds.