Many people contributed to the discovery of DNA, but there is one issue that still causes debate in scientific circles, and that is the discovery of the DNA molecule's twin-helix three dimensional structure. While Watson and Crick are generally credited with this discovery, and were given the Nobel prize for it, Rosalind Franklin, who worked in Crick's lab, probably should be credited with having made the actual discovery. However in the early 1950s women were still uncommon in research labs, and she was not given credit. Franklin died in 1958 and her work was not brought to public attention for many decades.
It is somewhat up for debate how many people "discovered" DNA, but the double helix is the most famous discovery. Here is a link to the work of James D. Watson and Andrew Berry.
Here is another perspective.