from the Wikipedias. I especially like the parts about the importance of a "prepared mind".

One aspect of Walpole's original definition of serendipity that is often missed in modern discussions of the word is the "sagacity" of being able to link together apparently innocuous facts to come to a valuable conclusion. Thus, while some scientists and inventors are reluctant about reporting accidental discoveries, others openly admit its role; in fact serendipity is a major component of scientific discoveries and inventions. According to M. K. Stoskopf[4] "it should be recognized that serendipitous discoveries are of significant value in the advancement of science and often present the foundation for important intellectual leaps of understanding".

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Most authors who have studied scientific serendipity both in a historical, as well as in an epistemological point of view, agree that a prepared and open mind is required on the part of the scientist or inventor to detect the importance of information revealed accidentally. This is the reason why most of the related accidental discoveries occur in the field of specialization of the scientist. About this, Albert Hofmann, the Swiss chemist who discovered LSD properties by unintentionally ingesting it at his lab, wrote

It is true that my discovery of LSD was a chance discovery, but it was the outcome of planned experiments and these experiments took place in the framework of systematic pharmaceutical, chemical research. It could better be described as serendipity.

Another example of Serendipity in science is associated with Alexander Fleming and his discovery of penicillin against the serious diseases at the time. He accidentally left a petri dish of Staphylococcus bacteria open and a mould had got inside which had appeared to have killed around the mould. It turned out that it was the fungus Penicillium and he turned the fungus into a groundbreaking anti-biotic.
The French scientist Louis Pasteur also famously said: "In the fields of observation chance favors only the prepared mind."[5] This is often rendered as "Chance favors the prepared mind." William Shakespeare expressed the same sentiment 250 years earlier in act 4 of his play Henry V: "All things are ready if our minds be so."