Wilde was born in New York City on March 10, 1984. Her mother, Leslie Cockburn (née Redlich), is a 60 Minutes producer and journalist. Her father, Andrew Cockburn, who was born in London, England, and raised in Ireland, is a journalist, as are her uncles Alexander Cockburn and Patrick Cockburn. Her older sister, Chloe Cockburn, is a civil rights attorney in New York; her late aunt, Sarah Caudwell, was a writer, and her paternal grandfather, Claud Cockburn, was a novelist/journalist.

Wilde has appeared in the films The Girl Next Door, Alpha Dog, Conversations with Other Women and Turistas. She became known for her role on The O.C. as Alex Kelly, although she originally auditioned for the role of Marissa Cooper. She has also appeared in the Dashboard Confessional music video for "Stolen", and the French Kicks music video for "So Far We Are". She was strongly considered to play Bond girl Vesper Lynd in the 21st Bond film Casino Royale but Eva Green eventually won the role. In 2008, Wilde was honored alongside Jesse Eisenberg with the Vail Film Festival Rising Star Award.