There is plenty of advice on what produce should be washed before cooking with it. For example, a bag of salad greens doesn't need to be rinsed again before adding to a recipe, if it is labeled as pre-washed or triple washed. You may assume that any produce that's going to be peeled before using doesn't need a rinse, either. After all, you're peeling off any leftover dirt, right? However, you need to wash that fruit or vegetable before peeling it.
Many of the fresh products we buy have measures built into its packaging to help decrease exposure to bacteria and other germs, such as that absorbent pad found in meat trays. Once it enters your kitchen, though, you still need to be vigilant about potential cross-contamination between the food and any gadgets or cooking surfaces used. It's possible to spread dirt and other unsanitary elements from your kitchen knife or peeler onto the freshly peeled produce, so a rinse before cutting off any part of the produce prevents the unnecessary migration of germs.