These are the characters whose moral standing is kept in the dark. Maybe they work for the Big Bad, but don't do anything really evil themselves. Perhaps they are Wild Cards who use the Heel Face Revolving Door constantly. Or maybe they are Evil Overlords who can seriously claim to be Reasonable Authority Figures. But one thing is certain: until they do something truly heroic or heinous, placing them somewhere in the Character Alignment is a wasted effort.
Sometimes, the writers will deliberately leave it to the audience to decide what their true colors are.
In Neon Genesis Evangelion, we have Gendo Ikari, who, at the start, keeps it unclear whether he does care about his son, Shinji, and the world's safety or not. In the end, we learn that it's neither, he's just obsessed with bringing back his wife and will use any means to do it.
That's debatable - While he doubtlessly puts getting his wife back before anything else, the way he justifies his actions in episode 25 suggest that he genuinely believes that his version of the Human Instrumentality Project is the only way for humanity to survive, his final words make it pretty clear that he did care about Shinji, but happened to have the very same self-esteem issues Shinji has, and the same can be argued for Rei (given that Fuyutsuki, usually the more moral/sentimental of the two, calls him out on getting to attached to her), and he still opposes the actual villains of the show with the goal of doing what he thinks is protecting mankind, ultimately making him more of a Byronic Hero
This is the whole premise of V from V for Vendetta. Hero or terrorist? Or both?
In Watchmen, it's left largely up to the reader to decide whether Ozymandias' master plan was truly the right thing to do.
Same with Rorschach. He is deliberately left morally ambiguous to let the readers decide whether his extreme methods of fighting evil were necessary or not. Or whether exposing Ozymandias's plan was the right thing to do or not.
Discworld's Lord Vetinari is a Magnificent Bastard par none, who keeps Ankh-Morporkh's nobles in check through manipulation and intimidation. He is also a former Professional Killer to boot. Apparently, he got into his position thanks to a few well-thought-out assassinations and a firm belief that Humans Are Bastards. He's also the most competent and benevolent patrician the city has ever had.
Severus Snape of Harry Potter fame is the poster boy for this trope. His true allegiance is revealed only after
Varys from A Song of Ice and Fire. When most of the characters are busy grabbing as much power for themselves as possible, Varys seems to be the only one who actually cares about the realm and it's subjects. While he hates the selfish and power hungry nobles, he is also willing to throw good...well, goodish characters to the wolves. What he wants and why is yet to be revealed.
Mad Men's Bert Cooper is not afraid to resort to blackmail to get his way, and has threatened to lock someone who disagreed with one of his schemes in a closet for a weekend if he didn't comply. Another character believes that he has arranged for someone to be killed before. However, it is never made clear if he intended to follow through with his threats or if he really had that person killed. He always comes off as a kindly, albeit eccentric, old man.
Pokémon Black and White's Team Plasma is this for roughly five minutes. Ghetsis' speech does make sense, but they are the shady organization in a Pokémon game. Then we see one of their grunts kicking a Munna. N does keep his ambiguous status till the end when we learn that
Flemeth from both games. She dismisses rumors without confirmation or denial, and there hasn't been a witness to or onscreen demonstration of her villainy. She's done more to assist the heroes, and her battle with the Warden was only in self-defense. Her power is said to come from demonic possession, yet neither her motives nor methods match any other examples. Morrigan discovers a ritual that supposedly permits her to possess others, but the reasons and results for using it have been cast in question.
Her daughter does follow in her footsteps. Despite sticking with the Warden for the entire game
Also, the only one who reads the book where the ritual to possess others is mentioned is Morrigan. Who also seems concerned if you had read it before, and is just as morally ambiguous as her mother, which makes the whole thing rather suspicious.
The Spathi of Star Control 2 are a textbook example. They fight for the Ur-Quan and don't seem terribly upset about being party to the enslavement of all intelligent life, but while spineless and shifty they never come close to doing anything evil.
The Arilou are a somewhat more benevolent version. They clearly care about humanity, though their reasons for doing so are left ambiguous. They are also The Greys, and have done experiments on us throughout our history, again for purposes they are reticent to discuss. And while they joined the Alliance, they abandoned it as soon as it became clear that the human race was "safe" (i.e., safely enslaved), and were unconcerned with the fate of their other allies.
The Orz. Weird Starfish Aliens whose language we can't properly translate. They are quite friendly, and will gladly ally with humanity...but there's something a little bit sinister about them. You meet them in Androsynth (evil cloned human) space, with no sign of the Androsynth anywhere. Demanding answers from the Orz as to what happened is their Berserk Button, and they will attack if you keep bringing it up. The Arilou (see above) insist they are dangerous, and vaguely dole out Eldritch Abomination / Cosmic Horror Story implications. It's all surprisingly creepy.
Most of the witches in Umineko no Naku Koro ni fall into this category as suits their whims, leaving it quite difficult to tell which if any of them is evil, good or simply in it for shits and giggles.
Of the six members of Order of the Stick, Vaarsuvius is the most morally ambiguous. Vaarsuvius is condescending and arrogant and doesn't really care much about saving the world; s/he just joined the Order in pursuit of Arcane knowledge and power, and is trigger happy in his/her use of magic. But s/he genuinely cares for the rest of the Order, and is appalled by Belkar's psychopathy.
Not to mention V had recently shown to be quite... abusive, towards a dominated foe. Though it is a bad guy under V's control, if there were laws on how a dominated enemy can be treated, V would've broken more than a few of them in just two strips.
On the other hand, V seems to be drifting more towards the "Good" end of the spectrum lately, courtesy of several My God, What Have I Done? moments.
In Girl Genius, Baron Klaus Wulfenbach starts out as a villain who has conquered most of Europe. The reason he did this was to keep in check his fellow mad scientists, who were mostly waging an everyone-against-everyone war on ruins of a halfway-happened Zombie Apocalypse when he crashed the party.
Jägers are mostly considered nightmarish monsters outside of their masters' land -- where they are, conversely, mostly considered heroes. The sorts of people who chose the transformation and indefinite active military service are obviously dangerous, but "good sports" and honorable in their own strange way. Most are not actively malevolent -- one is, but he "iz no longer a Jäger". Still, their word for a Heterodyne who choose good over evil is "boring".
On Galtar and the Golden Lance, Rak and his son, Tuk, are mercenaries who serve either Galtar or Tormack, depending on the circumstances.
Zuko from Avatar: The Last Airbender starts out this way. He is the first antagonist, but is given enough sympathy points through out the first season that it is more than a bit hazy on which side of the fence he'll wind up.
Its sequel series, The Legend of Korra, follows the tradition but alters the execution - the masked and compelling Amon has a sympathetic backstory told by himself, a number of legitimate points, a mysterious and horrifying ability that he's thus far only used on the deserving and a meticulous, effortless brand of manipulation that throws everything he says and all his motives into question.
On Adventure Time,Marceline was this trope in at least her first few appearances, where it was sort of unclear if she was actually going to start killing people or was just messing with Finn and Jake. More recent episodes portray her as basically good, if somewhat mischievous and perhaps capable of true nastiness.
In Warhammer 40000 this is the Alpha Legion's hat, down to the last man. While they sided with Horus during the Horus Heresy, they were apparently attempting to fulfill a prophecy in which Chaos would be destroyed permanently (at the cost of the human race albeit). After the Heresy, they're the only legion not present in the eye of terror, and are generally planning something...