Since joining the sketch comedy series in 2005, the comic has become known for portraying the sociopathic schoolgirl Gilly, the manic Target Lady and Amy Poehler's endlessly-annoyed Aunt Linda.
In an interview with The New York Times, Wiig noted that she enjoys exploring the more bizarre aspects of human nature.
"I never think of [my characters] as annoying," she insisted. "If I had to put them in a category like that, I would just say a lot of my characters are that person at a party that you don't want to talk to, because maybe they're talking too much. It's fun for me to play people that are just kind of odd."
Her Saturday Night Live boss, long-time executive producer Lorne Michaels, told the paper that he ranks Wiig in the "top three or four" performers in the history of the legendary show because of her creativity and level head.
"An old shrink of mine would say she doesn't spill over," Michaels joked. "There are people who I have worked with… who are always in some state of crisis: their boyfriend left, their agent is lying. What I'm getting at is [her] still waters run deep."
Saturday Night Live returns this weekend with host Tina Fey and musical guest Ellie Goulding at 11.30/10.30c on NBC.
Wiig will appear on the big screen with co-stars Maya Rudolph and Ellie Kemper in Bridesmaids, which is released on May 13 in US cinemas and on June 24 in the UK.
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Watch a trailer for Bridesmaids below: