Shampoo that claims to help grow new hair: scam or not? For the most part, this is a scam. The great majority of hair loss in men and women is caused by a hormonal variant of testosterone in the scalp called DHT, which stands for dihydrotestosterone. DHT is made in the body when an enzyme called 5 alpha reductase acts on testosterone. Excess DHT in the scalp causes hair follicles to shrink slowly and die. This can happen in women too, but to a lesser degree since women naturally produce much less testosterone than men do.
Hair regrowth products are a category where scams flourish. Everyone wants a healthy, thick head of hair, and sometimes our emotional attachment to the idea of having that overrides our natural skepticism of big claims from a product we've never heard of. Hair regrowth treatment is a thriving industry, and there are numerous ways of coping with hair loss. Everyone's first preference would be natural hair regrowth, but this is not always possible.
The drug Propecia is a 5 alpha reductase inhibitor. It is taken by mouth, and started out as a drug for treating prostate problems. It had some side effects that were bad (such as loss of sex drive) and some that were good, the primary one being slowing, halting, or even reversing hair loss. It is now available as a daily drug for this purpose by prescription. For those for whom Propecia works, it is a highly satisfactory method of having natural hair regrowth. 
As for topical products, the drug minoxidil is available over-the-counter as a solution that is applied to the scalp daily. It has been approved by the FDA for treating hair loss. It has few to no side effects. The results aren't always very noticeable, but it does cause new hair to grow. 
Other hair regrowth treatments vary in their effectiveness. Hair regrowth supplements get mixed reviews as far as effectiveness, and male hair regrowth shampoos are much the same. While it is important to treat the hair you have well so that it won't break and so that it will grow as well as possible, shampoos claiming to regrow hair should be evaluated with skepticism. One product, an over-the-counter shampoo called Nizoral, has been shown in preliminary studies to reduce levels of DHT, and in some cases stop or reverse hair loss. It has not, however, been approved by the FDA for use as a hair loss treatment, but for those who are encouraged by the anecdotal data, it is a possibility.