Though many of Arnold's classmates have A Day in the Limelight, Sheena never received her own episode.
Nadine was pretty much ignored unless she was around Rhonda despite having an established personality in her few appearances and being featured prominently in the show's opening sequence. According to the leaked plot details of the original Jungle Movie, Nadine would finally be fleshed out a little more, but the revived film did not do this, as Nadine only has a couple of lines, though her bugs prove useful when escaping from the pirates' clutches.
Many of the boarders who appeared only in season 1 such as Lana Vail, Mr. Purdy, and Mr. Smith could've been good characters had they lasted the show's run. Later seasons imply that they all moved out. The former was supposed to be more fleshed out, but considering what Bartlett supposedly had planned for her (an implied pedophile who would frequently flirt with Arnold), it's lucky that it never happened.
Ruth has this status with some fans, especially those who preferred her over Lila. She even had some ship teasing with Sid in "Operation Ruthless" and "Hey Harold!", it's a shame that it never amounted to anything.
Torvald only made two appearances despite apparently still being in Arnold's class (he isn't usually seen in classroom scenes). What's worse is that his role as the older kid Held Back in School was given to Harold despite being in preschool with the other kids and clearly looking younger than Torvald.
Suzie never really played much of a role in the series other than as a Satellite Love Interest to Oskar.
We never found out who was Fuzzy Slippers, Gerald's mysterious informant.
Chloe from "Gerald Vs Jamie-O" could have been a potentially interesting character if the reasons behind her desire to be seen as "mature for her age" enough to snag an older guy for a boyfriend were explained, but the episode ended without any such explanation and Chloe never reappeared except for a cameo in the Movie.
After all the trouble Arnold and Helga went through to find her, Mai Hyunh never appears after "Arnold's Christmas" and is only mentioned once more in "Family Man", which was in Season 5. She does return in The Jungle Movie, but only as a background character.
Word of God mentions that Lila has a dark side she keeps repressed, much like how Helga represses her good side, but this is never actually explored, even though doing so would have made Lila a more interesting character and a more sympathetic one since how and why her dark side was born would be very obvious to anyone who had watched her debut episode. But sadly we're stuck with just a straight Pollyanna rather than a deconstruction of one. Only in "Timberly Loves Arnold / Eugene Eugene", her last appearance in the show before she was Demoted to Extra, do we get any hints at Hidden Depths, and, you know, it was her last major role, so it was too little, too late.
Dr. Bliss never makes another appearance after "Helga on the Couch" even though finally providing an aversion to There Are No Therapists and giving Helga much-needed psychiatric help. Their sessions might have provided even more character development for Helga, eventually resulting in her dropping her Jerkass facade in favor of a more healthy approach to her struggles. What makes her case stand out is that, unlike many Darkhorses who disappeared without explanation, she did not come Back for the Finale (not that there would have really been a reason for her to do so). She does, however, promise Helga more sessions at the end of the episode, implying that Helga still sees her offscreen.
This also applies to Big Bob and Miriam Pataki to an extent. As episodes such as "Quantity Time" and "The Beeper Queen" demonstrate that they are capable of recognizing their poor treatment of Helga and improving their behavior to be better parents for her. Unfortunately, due to the status quo is god nature of the show, they rarely retain these realizations and more often then not, revert to their default characterization.
The only time that Iggy ever got a spotlight was in the hated "Arnold Betrays Iggy". He was never used again after that episode, most likely due to negative fan reaction to the character after this episode. However, some feel like they wasted a opportunity to try to redeem the character after that episode, especially since they thought that it was more Sid and Stinky's fault for the incident rather than Iggy's.
One of the leaked plot details of the original Jungle Movie was that Nadine was supposed to get her own subplot after never having had a single episode that focused entirely on her. Needless to say, fans of hers were a bit miffed that it didn't happen. The writers probably couldn't figure out a way to write it in without taking attention away from the main plot.
Despite her reputation in the fandom, many are also upset that Lila was once again a voiceless background character in this film, without any definitive closure being given for the Arnold/Lila/Helga love triangle that ended so abruptly in "Timberly Loves Arnold/Eugene, Eugene!" This was a decision made by Craig as he did not want her getting in the way of Arnold and Helga, but he jokingly (or maybe not) said in a live chat that Lila may return as a full-fledged character if the series is revived.
that Lila may return as a full-fledged character if the series is revived.