Detective Gumshoe started off as a scatterbrained but reliable ally to Phoenix Wright (defense attorney), even though he was usually under the thumb of Miles Edgeworth (prosecutor). As time went on, Gumshoe progressively grew ditzier and can't even solve simple logical problems, relying on Phoenix and the prosecutor of the week to solve everything.
Maya Fey grew incredibly ditzy over the series as well. In the beginning, she did all she could to help Phoenix on his cases, even if she wasn't always right, and didn't have any useful skills apart from the ability to channel her dead sister's spirit (which, due to her incomplete training, wasn't always reliable). Afterwards, Maya uses off the walls logic to justify her reasoning (which usually didn't solve anything and annoyed Phoenix) and always goes on about food at inappropriate times, turning her into a Cloud Cuckoo Lander.
Pete Wheeler of Backyard Sports. I mean, he forgot how to ride a bike within a few months of being a pro.
Yasuhiro Hagakure of Dangan Ronpa was never very bright, but over time his actions and dialogue become increasingly more erratic and idiotic. This is lampshaded in the following exchange between him and Aoi Asahina.
Hina: "What the heck's happened to you...? You weren't like this from the beginning, you know."
Hiro: "Well back then my personality hadn't quite solidified yet...!"
Yuna too although to a much lesser degree as it mostly takes the form of her naivety growing up on a small isolated island sheltered from life by her peers. It is also implied in-game that her new-found idiocy is due to the fact she is trying to imitate Rikku.
Perhaps it was just Kazushige Nojima's shaky writing (he admitted in an interview that he didn't do a lot of work on the first game and wasn't familiar with the plot/characters/cosmology of KH), but Sora went from often naive in Kingdom Hearts to often ridiculously clueless in Kingdom Hearts II.
This can probably be explained in-story by the fact that he just spent a year in a coma, having his memories and certain parts of his personality recompiled basically from scratch. You're bound to have a bit of brain damage from that.
Tomb Raider has Larson Carraway, a hired henchman who has a redneck accent and wasn't too bright, but he wasn't a complete idiot either. By Tomb Raider Chronicles, his character is retconned to become even dumber (he tries to shoot Lara from a rooftop instead of letting her get the MacGuffin(s) so that their work is made easier) and his accent sounds like a redneck even more.
The Avatar from the Ultima series suffers an extreme case of this in Ultima IX, where he seems to have forgotten everything about Britannia, since he keeps asking about things he should know about since previous games. The most famous of these questions seems to be "What's a paladin?"
Sonic the Hedgehog: Knuckles. Ok, he was never the sharpest tool in the shed but that was more due to naivete and lacking sort of social skills, and even then had enough sense to stay on task and get the job done. Over time though, his lack of intelligence was played up to the sacrifice of all of his other traits which led to this trope. Almost all of his appearances nowadays(With the exception of his comic appearances) emphasize his lack of intelligence above all else.