"Serendipity is looking in a haystack for a needle and discovering a farmer's daughter."

From Wikipedia: selected examples of serendipity in science and technology:

• # Scotchgard moisture repellant used to protect fabrics and leather, was discovered accidentally in 1953 by Patsy Sherman. One of the compounds she was investigating as a rubber material that wouldn't deteriorate when in contact with aircraft fuel spilled onto a tennis shoe and would not wash out; she then considered the spill as a protectant against spills.
• Another sweetener, cyclamate, was discovered by US chemist Michael Sveda, when he smoked a cigarette accidentally contaminated with a compound he had recently synthesized.
• The psychedelic effects of LSD by Albert Hofmann. A chemist, he accidentally ingested a small amount of it upon investigating its properties, and had the first acid trip in history, while cycling to his home in Switzerland; this is commemorated among LSD users annually as Bicycle Day.
• Discovery of the principle behind inkjet printers by a Canon engineer. After putting his hot soldering iron by accident on his pen, ink was ejected from the pen's point a few moments later.

Serendip is the old Persian name for Sri Lanka.