This is one member of a group of chemcials that curlies refer to as "sulfates" and it's usually abbreviated as SLS.  Chemcially speaking, they are detergents - just like the stuff you wash your car, clothes, and dishes with.  It's very harsh and stripping, and will even remove permanent hair color. 

Since we curlies work hard to keep our hair mositurized, using something like sulfates on your hair is very counter productive for 99+% of us.  We work so hard to get oil & moisture in to our hair. SLS has been accused of causing cancers but so far there isn't any real evidence of that.  It is a skin irritant and that irritation might theoritically lead to cancer.  Then again I could theoritically be hit by a meteor falling from the sky when I walk outside, too.  While I don't like it, there's no hard link yet. 

However, some animal studies have shown eye damage with using SLS.  In paritcular, the younger the animal, the more the damage.  Even more distressing is that these studies show that the damage can occur even when SLS isn't applied to the eyes, but to other parts of the body.  There are also other studies that show this is stored in the brain, liver, and other organs after the skin comes into contact with SLS. 

Because of the nature of the process that makes SLS, it is often contamined with nitrates.  These combine with compounds in tap water and other compounds in hair care products to form known carconigen, nitrosamines. 

I also find it disturbing that the OSHA required handling instructions for SLS say in big red letters "DO NOT GET IN EYES, ON SKIN, ON CLOTHING."  It also advises that this be handled with gloves and appropriate eye protection.  That's not very reassuring for something you're supposed to put on your head.

Furthermore, sulfates are leading reason that so many people have itchy skin and scalp.  I know that since I've gone sulfate free my bottle of dandruff shampoo hasn't been touched.  I made my boy friend do the same, and now his hasn't been touched either.  When I asked him about it, he shrugged and said "I haven't needed it."

References - Material Safety Data Sheet on SLS, Wikipedia article, Healthy Community Web Site