Keep in mind that these quirks needn't necessarily make your character utterly "unique" -- certainly not so different and unique that no one can relate to him or her. Yet in each quirk there should be a play on people's expectations, a twist of common stereotypes, or some irony that sparks people's interest.
Your character's quirk should also show what you most love about your character, and it should be a reflection of some quality that you love about yourself. While negative quirks can work well for antagonists in fiction, in roleplaying they tend to just put people off. Sociable quirks work better than anti-social quirks (such as throwing a fit, or sulking), though often good roleplayers can make their quirk an interesting flaw that draws other people closer to them rather than pushing them farther away. You may also have more than one quirk, as long as they work in harmony with one another, perhaps to balance out your character's behavior and prevent a flaw from overwhelming other people. Whatever quirk you choose, it should enable you to interact with others more, not less, whether for just a few minutes, or the entire span of time that you spend in World of Warcraft.
To help illustrate, here is my own favorite character's quirk, as well as a few quirks I have seen in other people's characters, each of which surprised and delighted me, and made me which I wish I had thought of that idea first:
"Grumpy? Vhat is ze meanink of zis vord?"
My current main is a draenei hunter, who, as I have mentioned before, speaks with a heavy accent. While this is in itself a "quirk," its real purpose is to set her apart as an obvious foreigner, and give her an opportunity to convey her inquisitive, innocent nature to others. When you talk to her, you may suddenly find yourself happily teaching her new words, or explaining some aspect of your culture that you never really thought about before. She radiates a friendly and welcoming feeling to everyone, founded in her own peculiar understanding of faith in the Holy Light. She is, in part, inspired by the "Twoflower" character in Terry Pratchett's Discworld novels, and like him, she never realizes she should be angry or afraid, always optimistic that things will work out in the end.
To a lesser degree, I also use the "PetEmote" addon to allow her enchanted pet to take part in any given interaction. Her grumpy old owl provides a counterpart to her positive nature, comically focusing on the negative side of things, or bantering with her in his Brooklyn accent. He helps prevent her from appearing so very holy and spiritual all the time that others get annoyed.
"Pockletock squeesh many orcs today!"
My gnomish warrior friend always talks about himself in the third person. With his odd grammar and limited vocabulary, he comes across as stupid and naive, maybe even mentally retarded. Yet he makes this an extremely lovable quality, because his player intelligently discovers the hidden irony in any situation, and uses his character's innocence to bring it out. Whenever he talks about "squeeshing" his enemies, I laugh inside, imagining his adorably diminutive character wielding enormous weapons, taking on enemies many times his size, and bonking them on the head.
"Happeh Skull Days!"
Another friend of mine plays an adorable troll warrior, also speaks with a heavy accent, but to an entirely different effect. When she sees you for the first time on any given day, she will announce that today is a "Skull Day" and give you an actual skull as a celebratory gift. The glee with which she handles such a morbid thing feels particularly trollish, and catches you completely off guard. If you don't know already, you inevitably ask someone else in her group... "What's a Skull Day?" Really it's just her own personal holiday, meaning that she's in a good mood, but it makes others feel as if its a real holiday -- and instinctually makes them feel the desire to celebrate "Skull Days" with her.
<Pushes his glasses back up before they slide off his muzzle>
Usually, we think of tauren as having more brawn than brains, but one druid friend plays his tauren as a lovable scholar. His simple action of adjusting his glasses makes him seem as warm and approachable as a teddy bear. In a sense, he is the opposite of my gnomish warrior friend -- a huge and monstrous, yet most intelligent and gentlemanly creature. He can discuss any subject at length, and provide some wise insight into any situation. I can almost feel the warmth of his smile when I chat with him.
<smiles, and brushes a lock of hair behind her ear.>
Although there are a lot of female characters on RP servers, many of them don't go in much for traditional femininity. One friend of mine plays a shy human mage who always listens politely, puts others ahead of herself, and uses short but sweet gestures to show how closely she is paying attention to you. She is proof that you don't have to be so very talkative or wordy to roleplay well. She can shine radiantly from the back of the room with a single and unobtrusive emote of an everyday action.
My final example comes from a gnomish mage I met once -- quite obviously a frost mage -- who had created a macro that let her sneeze and cast Frost Nova at the same time. After sneezing, she would then sniffle and say, "Excuse me! I have this perpetual cold!" and proceed to talk about any subject under the sun. I never saw her again, sadly, but I will remember her quirk for as long as I roleplay. Sometimes I mimic it with my bank alt, who is also a gnomish mage, though somehow I can't do it as well as she did.
Her use of the in-game spells as an element of her roleplaying was so brilliant that it struck me as an essential skill all WoW roleplayers should develop.
Have you known or played any very memorable characters? What special quirks have you noticed in them that immediately gave other people a sense of who they are?