Wired has an article on the best accidental discoveries, including X-rays, penicillin, and Silly Putty:

X-rays
Several 19th-century scientists toyed with the penetrating rays emitted when electrons strike a metal target. But the x-ray wasn't discovered until 1895, when German egghead Wilhelm Röntgen tried sticking various objects in front of the radiation - and saw the bones of his hand projected on a wall.

Penicillin
Scottish scientist Alexander Fleming was researching the flu in 1928 when he noticed that a blue-green mold had infected one of his petri dishes - and killed the staphylococcus bacteria growing in it. All hail sloppy lab work!

Silly Putty
In the early 1940s, General Electric scientist James Wright was working on artificial rubber for the war effort when he mixed boric acid and silicon oil. V-J Day didn't come any sooner, but comic strip image-stretching practically became a national pastime.

...via elearningpost