Inventions that were created by mistakes
Plastic
Can you imagine carrying water bottles made of clay or using disposable utensils made of eggs and animal blood? The legend of the discovery of plastic says that were it not for two accidents, those might be the materials we'd be stuck with today.
The first tale starts in the lab of Charles Goodyear (yes, thatGoodyear), who combined rubber and sulfur and accidentally put it on the stove for a period of time. When he came back, he found a tough and durable material--created through a process eventually called vulcanization.
The second was a spill in John Wesley Hyatt's shop. Inspired by a $10,000 contest to find a replacement for elephant ivory in billiard balls, Hyatt accidentally spilled a bottle of collodion, only to discover that when it dried it formed a flexible-yet-strong material. He didn't win the contest (nor did anyone, for that matter), but by 1872 his brother Isaiah coined the term celluloid to describe what was becoming the first commercially successful plastic-even used in the first motion-picture film used by George Eastman.
Penicillin
Starting in the late 19th century there had been many accounts by scientists and physicians on the antibacterial properties of the different types of moulds including the mould penicillium but they were unable to discern what process was causing the effect.
The effects of penicillium mould would finally be isolated in 1928 by Scottish scientist Alexander Fleming, in work that seems to have been independent of those earlier observations.
Fleming recounted that the date of his discovery of penicillin was on the morning of Friday 28 September 1928. The traditional version of this story describes the discovery as a serendipitous accident: in his laboratory in the basement of St Mary's Hospital in London (now part of Imperial College), Fleming noticed a Petri dish containing Staphylococcus that had been mistakenly left open was contaminated by blue-green mould from an open window, which formed a visible growth. There was a halo of inhibited bacterial growth around the mould. Fleming concluded that the mould released a substance that repressed the growth and caused lysing of the bacteria.
Once Fleming made his discovery he grew a pure culture and discovered it was a Penicillium mould, now known as Penicillium chrysogenum. Fleming coined the term "penicillin" to describe the filtrate of a broth culture of the Penicillium mould. Fleming asked C. J. La Touche to help identify the mould, which he incorrectly identified as Penicillium rubrum (later corrected by Charles Thom). He expressed initial optimism that penicillin would be a useful disinfectant, because of its high potency and minimal toxicity in comparison to antiseptics of the day, and noted its laboratory value in the isolation of Bacillus influenzae (now called Haemophilus influenzae).