In addition to holding our faces on our heads, our facial skin creates a waterproof barrier that protects us from the dirty, dangerous world around us. This is accomplished in part through the production of oil called sebum. This oil is produced by tiny sebaceous glands that exist midway down the shafts of our hair follicles. As sebum travels up and out of the hair follicle, it mixes with sweat and dead skin cells that are also migrating up the follicle. Upon reaching the surface of the skin, this mix (now joined by other lipids such as linoleic acid) spreads out and hardens, forming an armorlike coating that helps prevent bacteria and other invasive agents from penetrating the outer layer of skin.
However, when external dirt builds up or there's increased production of oils or skin cells, blockages occur in the follicles. The mix of sebum, sweat and dead skin cells continues pushing up against the blockage and growing larger, creating a growing traffic jam in the follicle. Once bacteria arrives on the scene and inflammation occurs, you've got acne. Without washing, acne breakouts and blemishes occur, regardless of the cleanliness of your environment.
When we wash, we clear our pores of debris and prevent the excessive buildup of this oily armor, allowing the outwardly mobile skin cells and lipids still in the follicles to emerge unimpeded to form a new layer of armor on the surface. (But we can't undo existing acne, only prevent future breakouts.)
If you stopped washing your face entirely, your pores would become clogged and stay clogged. You would experience lots of acne (likely some mix of whiteheads, blackheads and cysts), blotchy skin, redness and irritation, and skin that looked dirty, oily and greasy.
The incredible itchiness you would experience would force you to scratch at it like crazy, possibly leading to broken skin and the risk of infection (which wouldn't be an entirely small risk since you've completely stopped washing your face).
Now that we've put your question to rest, click over to the next page for more articles on cleansing that dirty mug of yours.