Until Apollo Justice hit the market in America, Ema Skye appeared in all of one case (albeit a big one) in the first game as a stand-in for Phoenix's assistant, Maya. However, she apparently struck a chord with people, given that her coverage practically eclipsed Maya for a while — maybe it was the magenta goggles and flair for scientific investigation. She was almost the protagonist of Investigations before a certain cravatted prosecutor took over.
Don't forget Matt Engarde, who only appeared in ONE case, but has a huge fanbase. His rival, Juan Corrida, was just the victim of the case, and he has gained loads of fans (though this may be because of fanartist Zarla's works).
Byrne Faraday of Ace Attorney Investigations has also become very popular, despite the fact that we see exactly one screenshot of him before finding his corpse. Probably has something to do with being a good father to Kay, a master thief, and one of the very few prosecutors who isn't an Amoral Attorney.
Detective '''Badd'''ass in Investigations. You know you're popular when you're the Ace Attorneyequivalent to Chuck Norris.
Luke Atmey from The Stolen Turnabout. He is one of the most popular one-shot characters in the series and easily the most popular character introduced in Trials & Tribulations after Godot — yes, even more than Dahlia. There are even entire fansites dedicated to him.
Despite their connections to one of the most hated cases in the series, Turnabout Big Top, Acro, and Max are quite popular with the fandom. Unfortunately, the same cannot be said for Moe and Ben & Trilo (maybe Ben, but definitely not the other two).
As for the students themselves, the first game has popular characters such as Kiyotaka for his earnest attempts to uphold the group dynamic and keep people working together towards a common goal, Chihiro for being a Moe character, his status for having a Small Role, Big Impact, and his Hidden Depths, Hina due to her personality, her love for donuts, and being one of the nicest surviving characters in the game along with Makoto, and Sakura due to her Heroic Sacrifice which counts as a Crowning Moment of Awesome.
As for the second game, some of the most popular students include Sonia due to her being Sophisticated as Hell as well as her love of morbid things like blood sacrifices and serial killers, Ibuki for her design and upbeat personality, and Gundham for being a hammyCloudcuckoolander that presents himself as an Evil Overlord and secretly wants to have friends.
The release of Unlimited Blade Works, however, may also put Lancer in this position. After the release, a lot of message boards (those who played UBW) were saying "Lancer is more GAR than Archer!" And yes, he's never alive by the end of any scenarios like Archer.
Rider as well. It's too bad she gets so little screen time even in the route focusing on her and Sakura as the heroines.
Playable Caster of Fate/EXTRA likely qualifies. She's barely promoted at all, but she's only a little behind Saber in terms of popularity in Japan, and probably surpasses her by a large margin in the west.
To a more minor degree, Assassin. Many people find his calmness and his katana and the way he was able to stand up to Saber despite his limitations far more awesome than any of the above. And then, of course, there's the music that plays during his fight with Saber in the Fate route.
Yuki for numerous reasons. The main reason is that he's the nice guy to Makoto's jerkass personality and probably the only sane man that is genre savvy enough to realize what's going on. He can call Sekai out on everything she's done to Kotohana and punch Makoto for being a dick. Finally he's the cross dresser that many guys have deemed more attractive than the girls of this series.
Black Battler; despite being an illusion created by Bernkastel, he's gotten popular enough to join the roster of the fighting games.
For the fans of Tsukihime, Nrvnqsr "Nero" Chaos and Satsuki "Sacchin" Yumizuka seem to be well liked, with the former due to his badassness and the later for her cuteness and unfortunate fate both in-game and metawise.
Sola seems pretty popular with the Sunrider fanbase, despite not having appeared in the game proper.