From about 53- 5 million years ago, Carcharodon megaladon, a shark believed to have grown to 60 feet, is known to have lived. Megaladon is only known from fossil teeth (as a shark's cartilaginous skeleton rarely, if ever, fossilizes) which can be up to 6 inches tall. Scientists have estimated that it grew to about 40-60 feet in length, and it is believed to have been similar to the Great White Shark. Although the Megaladon is generally believed to be extinct, there is a very small amount of evidence that it may still live.
In 1873, the Challenger dredged several Megaladon teeth from the ocean floor. By analysing maganase dioxode that had built up on 2 of the teeth, 2 of the teeth were dating to be 24,206 and 113,333 years old (it has been suggested that the dating may have been innacurate; some have suggesed that the teeth were actually a few million years old), which would suggest that Megaladon and modern humans had existed at the same point in history.
In his 1963 book, Sharks and Rays of Australian Seas, David Stead reported an account that he had been told in 1918. Supposedly, fisherman had sighted a gigantic shark (they gave measures ranging from 115 to 300 feet long) that had begun tipping over crayfish pots. The fishermen also said that the shark was a white color. According to Stead, the men were not likely to make up "fish-stories", though I still find the account somewhat unbelievable.
Some people have suggested that the Megaladon may still survive in the ocean depths. Theoretically, a Megaladon might be able to survive off of giant squids and occasional sperm whales. One problem with that theory, though, is that Megaladon is believed to have lived closer to the surface. The idea of a surviving Megaladon is tantalizing, though unless more substantial evidence surfaces, it seems likely that the shark is dead.