The Tokyopop translation of the Tokyo Mew Mew manga, which gave characters terrible catchphrases that clashed with their personalities (such as Ojou Minto's "Bust a move, girl") or just sounded awful (Ichigo's "Shocker!").
Likewise, to appeal to less traditional manga readers, the Viz Media translation of Hot Gimmick gives everyone vaguely Valley Girl speech patterns. While this sounds reasonable coming from the mouth of the teenage protagonist, coming from traditionalist middle-aged Japanese housewives? Not so much.
Speaking of Tokyopop, the OEL manga Bombos vs. Everything uses this trope liberally.
DiC and Cloverway who licensed the Sailor Moon dub at separate times were Mis-blamed for what was actually the actions of the sub-contracted dubbing company Optimum, who was responsible for most of the slang, as part of their marketing was based on the fact that they would add "correct" slang and cultural references. (DiC could arguably have sued them for false advertising.) It's also why the practice continued with Cloverway. Take for example this line from DiC's Sailor Moon dub:
"Serena:" This contest is going to be major boss, Luna!
This leads to wrong, wrong characterization. Michiru, Haruka, and Setsuna are characters who would never use slang in the Japanese version, but here they are saying "Hey girlfriend!" and "You look like the bomb in those kimonos!"
Several other examples, like "Wicked cool," "the bomb", etc. "Hunkasaur" was used to describe a cute guy several times.
Also from the Garlic Jr. arc: "Totally crampin' my style!" or "What a bummer!"
Z has other examples as well, even in the superior re-dubbing of the first 60-some episodes - though they usually aren't quite as bad as the above. Krillin is the usual culprit, having actually said "totally radical" at least once, and describing Goku as "one bad dude".
Yes. That's right, boys. Mondo cool.
Yamcha: Vegeta was crying? THAT'S WACK!
Goku would use the word bummer a lot.
The narrator says the trope name word-for-word in the first episode of the Funimation Dragon Ball dub.
Demashita! Powerpuff Girls Z. Not too much in the way of speaking, but most of their motions seem ripped from '90s "thug4lyfe" gangsta rap videos.
Excel Saga had an episode where Excel and Hyatt had to be the teacher of a bunch of Delinquents who spoke in incredibly anachronistic slang. However, this was both in the original and intentional, as Hyatt actually questioned why they were talking like that.
The original Japanese version is making fun of the ganguro fashion fad, wherein Japanese girls bleach their hair, tan their skin, and wear lots and lots of Day Glo eyeliner and lip gloss - all of which makes them look like a cross between the stereotypical California Surfer/Valley Girl and some sort of monstrous crone. Not surprisingly, this is also parodied with Jynx, which is also modeled off of the Yama Uba (Mountain Hag).
Chrono Crusade (the English dub at least) uses slang from the 1920's such as "Jake" instead of "cool" or "fine". Justified, though, because the setting is New York City in 1928.
There is Nunally's in one of the dubbed Picture Dramas: when trying to talk like a boy (it was the Crossdressing Festival), she comes up with "Radical, dudes!". Between her attempt at a masculine voice and the picture accompanying it, it came off as adorable rather than annoying.
Taken to the logical extreme in the BBT Abridged Movie, Jaden uses slang so often that Yusei has to translate for Yugi to be able to understand. Also; he raps.
Yuma, main character of Yu Gi Oh ZEXAL has his own arsenal of awfully (or perhaps awesomely) corny phrases. As dubbed in English, they include "Time to high-five the sky", "Get set to get decked", and "I'm feelin' the flow!" His optimistic lingo tends to irritate others at first, then work its way into their hearts.
Rad, of Transformers Armada is infamous for his catchphrase "Wicked sweet!", as well as the meme "I want to tell you about the Transformers!"... and, well, just look at his name.
The infamous 4kids dub of One Piece changed the original Japanese opening (which they even had translated) into a rap song. A very bad rap song.
The Mahou Sensei Negima! manga has this problem in a few volumes, depending on who's doing the translation. The first volume practically borders on a Gag Dub. Volume 5 is a little better, but having characters actually say "OMG" and "WTF" does not work well.
In the .hack//SIGN DVD exclusive episode "Unison," there is a lovely conversation between Balmung, who is an office worker in the real world, and Kite.
Balmung: This shindig looks like the bomb-diggity.
Kite: What did you say?
Balmung: What I mean is, it's not bad at all.
Interestingly the Japanese script had Balmung speaking normally: Kite's reaction is because Balmung praised Helba and her party, who previously only had his contempt
Balmung's English dub VA Crispin Freeman changed the line intentionally. It's a subversion since that was the effect he was going for.
Lampshaded/discussed in Bleach when Ganju, Ichigo, and Hanataro argue about whether certain slang is still current. This raises interesting questions, since Ganju and Hanataro live in a world resembling Feudal Japan. That said, Ganju is the leader of the local equivalent to a motorcycle gang, so whatever.