Commonly known as "skin tags."
Acrochordons are flaps of skin growth that can appear virtually anywhere on the human body; however, they seem most predominant in areas where the skin folds such as the neck, armpits, beneath the breasts, or any erectile tissue. They can be recognized by their loose, flat, and mobile nature (in that they can be wiggled back and forth on the connecting peduncle, or stalk) on the surface of the skin. In this regard, acrochordons vastly differ from stiff, round, immobile skin growths such as warts or moles.
This particular bit of information is important to know when you happen to have skin tags on your penis, and a public health official erroneously diagnoses your acrochordons as Human Papilloma Virus. This is also useful information in reassuring a skeptical new girlfriend (or boyfriend, or whatever).
They are not by any means harbingers of cancerous activity. Acrochordons are painless, harmless, and only slightly awkward in special social circumstances. They generally grow no more than half an inch at most, although there is one shady european account of a baseball-sized skin tag that, while still painless, apparently made cycling rather difficult. Most skin tags are very small and people who do get them often get more than one.
Skin tags start out as very small, soft bumps on the skin and evolve over time into the flaps of skin that hang down from their connecting points on the skin surface. They are more common in women than in men, though both genders see an increased chance of acquiring them at advanced ages. Occasionally they get irritated by bra straps or other sources of continuous friction and may twist: thrombosis may occur at this stage and make things painful. As with most internal blood clots, you'll want to get this checked out with a medical professional.
The acrochordon is a life-long gift your body gives to itself. Being that it is hereditary and not viral or in other means related to foreign malevolent organisms, it is obviously not contagious. If you experience irritation or undue embarrassment from it, they are easily removed much in the same way warts are: burning (cautery), freezing (cryotherapy), or just plain chopping with surgical scissors. It seems that after removal acrochordons do not regrow or scar; however, they may return elsewhere on the body for more fun.
Sources:
Encyclopedia and Dictionary of Medicine and Nursing, W.B. Saunders Co., 1972
http://www.skinsite.com/info_skintags.htm
http://www.nlm.nih.gov/medlineplus/ency/article/000848.htm
http://www.intelihealth.com/IH/ihtIH/WSIHW000/9339/28064.html
http://www.john-libbey-eurotext.fr/articles/ejd/8/8/587-8/
and several dermatologists who were probably getting tired of examining my penis.