Destroyer is a paramount of Renegade mentality... he thinks all alien are good for is cannon fodder. He reserves special hate for the asari, since they are pretty much women. Yeah, he doesn't like those either. They ain't good for anything. And I mean anything. He thinks Cerberus is actually pretty a-ok.
He isn't the most popular guy to have around, but nobody dares to say much to him since he's the best when it comes to weapon and his suit of armor is pretty frightening as well. I play him totally in black.
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Smashguard joined Cerberus because he wanted to do something good for humanity. He doesn't hate aliens at all and the more xenophobic elements of Cerberus always left a sore taste in his mouth. When TIM started going crazy he decided to leave, but but then, it was too late. They caught him and somebody he cared greatly about(haven't decided if that will be his brother or his boyfriend) and put him into Phoenix program. He got augmented against his will. His combat prowess greatly increased, but the toll was high. He carries the scars(think renegade Shepard) and uses his full concealment helmet most of the time to hide them from the rest of his unit. The person he cared about wasn't so lucky... they became one of the Dragoons. He escaped, but the guilt weighs heavily on him.
People don't really trust him, since you know... ex Cerberus. He's pretty indifferent about it... hell, he understand it. Still, when fighting Cerberus, the hate displayed has been known to leave people a little sick.
I play him as dead seeker. He uses Bonus Power option on charge and always charges, all the time, using Smash indiscriminately. Special hate reserved for Cerberus. He uses Harrier, one memento from his past... it reminds him of what he's done and how he failed. Plus, it's a pretty damn good gun.
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HFE and Demolisher are sisters, the former the elder one. The younger joined N7 because she always was a little of loose cannon, which shows now what with all the grenades she's carrying around. And while the older sister was always more of a traditionalist(married a nice guy from neighborhood, lost him when the Reapers hit Earth), the younger one was more wild. She has an asari lover, which is another point of contest between sisters. They just don't see eye to eye about these things.
Despite what it sounds like, they love each other a lot.
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Vorcha hunter is one of the few vorchas with a modicum of intellect. He was raised by an asari, which probably helped. When his surrogate mother was killed during the Reaper attack, he fled to Citadel, where he meet up with another orphan, as luck would have it, another asari. The two hit along and since times were tough, they concocted a scheme that would help them get by easier. They started going to casino, where the vorcha would enter a game of chance and the asari would give him hints. It was foolproof system, until they got caught. The group they cheated out of some credits came after them. They made a fatal mistake... they hurt the little one. Which caused vorcha to fly into bloodrage and murder them all... messily.
He was saved by Vega(yes, him) who recruited him into fight against Reapers in return for promise to shield the kid from further harm. Now, he fights wherever they need him.
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The Valkyrie... she has a rare genetic disease. It allows her to manifest an aura of biotic energy around her that harms everybody that comes near her. She is highly valued for this, even if somewhat of loner because when you can fry anybody just by being near you, you're not really popular. She is more than a little bitter, because while the ability is very useful, it is also very dangerous and taxing. Every time she uses it, she's chipping away at her remaining time in the galaxy. Given she's asari, she still has many centuries, but not nearly as much as many of her sister.
She is the demolisher's lover.
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Quarian male(haven't decided which one) is one of the last quarians in the galaxy, since my canon Shepard sacrificed quarians. He was an exile(not sure about charges either), which is why he survived. He... doesn't really know what to do with himself. He doesn't really hold it against Shepard, but he just doesn't know what to do now. Not enough quarians to repopulate... might as well strike it out with asari. At least that way, some of quarian qualities will be passed on.
Another potential death seeker.
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Paladin is the chain smoker. Seriously, with a voice like that, what did you expect? He is a polar opposite of the destroyer(the two often come to blows), since he values life in all it's forms and thinks we should just get along. No, he's not a hippie
When I play him, I try to use his shield as often as possible, since he also believes that it's his duty to protect others. I will stand before the teammate disabling the device, protecting him with shield.
Sadly, I don't get that chance often, since his tech combos are just too awesome 
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The vanilla asaridept is an unwanted draftee into the army. She didn't want to be in all of this, since she was just a civilian. Sadly for her, she was an incredibly gifted civilian, at least as far as biotics go. So, wanted or not, army it was. She was since then through traumatic ordeal, where she was saved by geth. It changed her perspective about the race and made her realize that she is indeed needed.
Character growth at it's finest.
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Geth engineer was a gift from the Consensus to the Alliance. He got assigned to a random soldier to show him around. The two build something of a friendship(after many zany and hilarious happenings) and the unit provided many technological advances that became of great use. He is the reason we now have geth scanner.
Also, since he got assigned the old Mantis rifle, the two became inseparable. It's the only thing he will use now and since he can stun enemies at will, it proved very lethal indeed.
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The asariguard... she's a party gal. With a wit and tongue to match. She's very popular amongst the troops and very unpopular with the chain of command. They send her on most dangerous assignments since they hope to get rid of her. She knows that. Everybody knows that. Unfortunately for them, she always seems to manage to get out of most troubles they get her in.
When you carry big gun(Claymore) and enough ordinance to blow a Reaper capitol ship sky high and have an attitude to match, that's not really surprising.
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Huntress is a polar opposite of the vanguard. Reserved and quiet. Comes with being one of the mostly highly trained and respected troops in asari army. She thinks the vanguard is a brute and a shame to everything the asari stand for. She's a little bit of a stuck up.
That's why it vexes her that more that their choice of armament is the same and that both of them are approximately on the same level of lethality, when it comes to enemies. She is pleased, however, that she doesn't have to resort to using grenades for that, but rather a fine biotic abilities that have been honed by centuries of training.
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Turian soldier is the veteran of many wars, including the one for Shanxi. He doesn't really hate humans(or any other race, for that matter), but he knows his place. If the order is given, he'll follow it. That's what being a turian is all about.
He doesn't really like his havoc counterpart. Too flashy and foolhardy, what with those jetpacks and... charging around? That's not the way the turians do it! You stand there and pulverize the enemies with firepower, not jump around like a pyjak on ryncol!
Still... he can't argue with the results.
I think that about covers it
Will add more of it later, if I can come up with anything.