Commercially grown produce is sprayed with wax, pesticides, chlorine derivatives, etc. You do want to wash to get a least some of it off. Ingestion of some of those things over time can't be good for you.
This all in addition to what Andrea is talking about for organic food.
Not properly washing vegetables is partially responsible for the spinach brouhaha a couple of years ago.
Well, I just ate some lettuce from my garden tonight. I washed each leaf individually and then gave them a whirl in the salad spinner...I still managed to get some grit in my teeth. I planted these myself, and used no chemicals whatsoever. I did, however, use manure to fertilize. Wash my fruits and veggies-you better believe it!
Personally, a little grit and dirt never killed anyone. Mark Sisson jokes about eating dirt but there is some merit to it, I think. It's not the grit that will get you, it's the chemicals that can throw you for a loop. So then you have to ask yourself, "is this clean dirt or chemically dirt?"
I try to buy organic and local grown food as much as possible. But sometimes you just can't so you deal and buy conventional crops. My general rule of thumb is that if it is organic, I won't bother washing it. I get my Spinach from Trader Joe's and it's been pre-washed. Maybe I'll find a bit of grit in there but I'm personally OK with that. What I'm not OK with is pesticides and chemicals so if I do have to buy conventional produce, THAT'S when I'll give them a rinse in the sink. My laziness overcomes my cheapness so I tend to go organic with anything that I will eat the peel (apples, carrots) and will save money eating conventional when I'm peeling it (oranges, the rare banana).
I wash to get rid of chemicals and embrace organics to circumvent that issue. Others, like Andrea, dislike grit and dirt and wash for that. To each his own.