According to the UC Berkeley Wellness Letter (June 2009), "before cutting a cantaloupe or any melon, wash it with cool running water and a scrub brush."
The article tells us that food poisoning from salmonella and other bacteria has been linked to melons, and if you cut right through the melon without washing and scrubbing the outside first, the bacteria can be sliced into the fruit.
They also add: be sure to refrigerate cut melon. Cut melon can be left out for up to 4 hours; after that, it should be discarded. If you're at a farmer's market, and you see cut melon for sale under non-refrigerated circumstances, don't buy it.