Even produce with a tough rind or peel (melons, peppers, cucumbers, potatoes, apples, pears, etc.) should be washed thoroughly, although you probably won't be eating the outside of some of these items. As a knife cuts through that outside rind or peel and touches the flesh inside of the fruit, it can transfer germs that will end up on your plate. To avoid that, use a vegetable brush and scrub the outside of these foods under running water.

More delicate fruits (like berries) don’t need to be scrubbed, just rinse them with cool, clean tap water.
Throw away the outer leaves of lettuce and cabbage, then rinse the inside leaves with clean water. Sprinkle salt into the water when washing vegetables. It will draw out insects.
Read these other tips for washing fruits and vegetables to ensure the fresh produce you eat is safe and clean.

For added safety you might want to try a commercial cleaner, like this handy Veggie Wash.
Note: Fruit will store longer if you wait to wash it right before serving.