It's not my most unique character personality, but I feel it's one of my crowning moments as a role player:
I spent time in a Star Wars campaign years ago. I played this slightly greying officer in a regional 'space navy' that was affiliated with (read, we took orders from, and they allowed us to not suck vacuum) the Empire, but not actually Imperial ships/gear. But my character worked more the rebel side of the law, as it were.
Game had run for about 6-9 months, and I did the things my character could, working to the extent of my abilities with the other members. I turn out to be the go to guy for negotiating, fast talking, and deal making. I was an excellent judge of character, and usually when I didn't trust someone, it came out that we shouldn't. I also got us and myself out of a few sticky situations... more than once they showed up to rescue me and I was already out. I occasionally got involved in fighting but being good rebels we pretty much only got into that situation when we were able to take people out hard and fast and get the hell out otherwise, though after I left the navy and started travelling with the rebels in their cargo modified troop transport, the found I was a damn good shot with the repeating blasters, and that became my battle post in the more common 'we're even/slightly overmatched and can't run away atm' battles.
So anyway about 6-9 months in, we get in WAY over our head on the ground (actually, we had snuck into an Imperial Interdictor) and gotten, well, not caught, but discovered and had our nemesis of the last 2 months after us. We were trapped, ready to make a stand vs. a 5:1 ratio of Imperial Troopers (not ST's but the non-elites), and the Bounty hunter was doing the 'old man, keep your head down I don't want to see it get shot off before mine when the blasters bolts start flying' thing.
I confidently pulled out my little navy issue blaster pistol that was an antique when the seperatist movement started, which was about good on the pistol range. Well maybe not there, it had a tohit penalty ( and seriously, it did less damage than the holdout blasters most of the party had hidden on their person), got in the front rank and waited. Here came our 'got all the stormtrooper training but got drummed out because he was too independant' nemesis in his custom armor, his navy troopers, and 4 Stormtroopers assigned to him.
Fighting starts after the usual threat/counterthreat. Nemesis ends up leading the move into position with his custom (force field equipped) armor, and the storm troopers using him as shelter. They get under cover where our cover is pretty much useless, and start pounding us, things look grim.
So I charge, jump over some obstatcles in the way, pulled my lightsaber out, took out two stormtroopers and knocked 'nemesis' and the others over with a wave of my hand. The proceed to block a 2-3 blaster shots from the troopers who start firing at the obvious target, the crazy old man waving a lightstick...
"You're a JEDI?" sums up the reaction from our Bounty Hunter, which due to being completely speechless loses his next turn of action because the GM asked him like 4 times what he was doing. Most of the party reacted similarly. Most of the NPC's too.. basically the GM gave me a surprise round in the middle of the combat.
I had been using the force the entire time, never really hiding it, just never advertising it. The GM went along. There was no note passing, just well understood things like 'I try to persuade him to look at things from our point of view', 'roll dice', rolls force persuasion check. I never used the word 'the force' except for other things (force points). I had even done some more overt force tricks both in view of the characters, and the players when I was out of sight, and they just didn't really pay attention because I was very low key about everything. (I thought the jig was up months ago... we got locked up in separate cells on a very lowtech planet.. physical bars and keys.. and as the jailer was walking away from my cell, last person in thanks to a suggestion about 'getting the dangerous looking ones locked up first, leave a harmless looking old man until the rest are taken care of' I did, in front of all the players, 'I try to get the keys off his belt without him noticing and the GM basically described me levitating them off the hook on his belt...) But I always had concealed, and never had used visably, my lightsaber. Though I had 'sliced' a few doors and locks. Well and some other things too...
In my quiet competance everyone assumed I was just some sort of slicer/con man type (think Lando) without the flashy moves. No-one knew I was a Jedi Knight late of the Old Replublic, on independant assignment headed to the outer rim when the orders came down to kill all of the Jedi (This was pre-ep 2, though enough spoilers were known at that point that the clones were the 'good guys'. But Order 66, even if the actual order wasn't know, was obvious to us from a Story standpoint).
Most unique would be difficult to pin down...
The vampire:masquerade character who was convinced he was really just plugged into some slick VR system (the base setting was V:TM in a future/semi-cyberpunk setting) was interesting, if a short lived game.
My 'kids get off my damn lawn' traveller bearucrat character who started his adventuring career at the spry age of 92... (You have a career, then when you get out you have skills and abilities and start 'adventuring'. you had to roll to be able to stay in your job and get more skills, otherwise you're fired, or you can not roll and just quit after a term. 'crats had a special rule that you have to roll every term, and if you succeed, have to stay in, even past retirement age. The target to stay in? 3+ on 2d6. Most 'crat characters die of old age before they get out.). He didn't cut through red tape, he phased through it like Kitty Pride, bypassing it all without disturbing it.
The conspiracy character (Imagine taking all the major 'conspiracy theories', tangling them up, mixing them into a coherant 'truth' (Aliens are here, some are in contact with governments, some just do horrific or not so horrific experments, others are preping the way for an invasion. The illuminati at least tries to be the secret government; they have several key government officials in each country, for example the majority of the US supreme court are members. There are chemicals in the water disguesed as purification and well being for mind controlish reasons, psychic and magic phenomena, etc.) and you've got this game) I had that was the uberScully. He didn't believe in any of that fantastic crap, and had never seen any rigerously tested evidence or believable testimony. Drove the other players nuts especially as I love reading that crap, and at the time listed to Art Bell while I was working nights (I know it's garbage, I just find it entertaining) so he could talk very knowlegably about the subject but had rational explanations for all of it. Mind you in his world, his rationallity was wrong.
In the vein of sceptics, I had a character in a Ghostbusters game that was an undercover agent for the EPA who got themselves hired by a Ghostbuster franchise to try to figure out what kind of chemicals they were exposing people to to inspire the so called 'ghosts' to appear.
There was that one... oh wait I don't talk about that one. nm.
An NPC I had in an 'anime themed' game I ran was a Magical Girl. Costume, wand, magic zappies, short speech length attack phrases, the works. Boring. Oh... she didn't know how to change back to normal, so she had to attend school in the costume... (And when she did get changed back, she did know how to transform into the costume again and something would come up...). Add the fact she was originally, and unwillingly, a Dark Magical Girl (bad guy) and that side of her could still be brought to the surface under the right conditions, and she helped the players live in 'interesting times'.
Somewhat cybered up merc in a cyberpunk game, his contract required he submit to cyber augmentation deemed neccessary to do the job, and accept cybernetic life saving measures to protect their investment if he was injured, and his religion (and he was quite religious) taught strongly that a) replacement of part of your body with artifical parts is a sin, even if it's for survival (artificial 'normal' heart), and b) breaking your word (and thus, contracts) was also a strong sin. They were kind of... more modern mennenites. Very conflicted character. Difficult to play well as I myself am not strongly religious.