For the last generation, the flea collar was by far the most popular form of flea control for household pets. At the time of their invention, flea collars were nothing less than a revolution in pest control, as they were the first flea control treatment that was easy for pet owners to use, relatively effective for extended periods and safe for pets to wear all the time. Safer and more effective alternatives are available today, making the flea collar somewhat obsolete and no longer recommended by most veterinarians, but the collar's popularity lingers amongst pet owners who have grown accustomed to the idea that every dog should wear one, as well as owners who can't afford the newer methods or remain unconvinced of their effectiveness.
The most common type of flea collar is a plastic collar, sized for a dog or cat and impregnated with slow-release pesticides designed to protect the pet for several weeks (which a lot of people take to mean "months", keeping old collars on their pets long after their effective protection period). The basic technology was invented by Robert Goulding, Jr. of Oregon State University's entomology department in 1964. Over the years, we've seen a variety of pesticides used in flea collars, but they are all similar in effectiveness and share a certain set of problems.
The greatest of these problems is the dispersal of the pesticide. Since it's released very close to the animal's face, the pesticide has to be limited in strength or it becomes a significant health risk. Its effective protection zone is therefore limited to the front half of the animal, with very limited effectiveness around the hindquarters.
Now, you may think that limited protection is better than none, but it's really not. Flea control is an all-or-nothing issue, because if half your dog is unprotected the fleas still have a viable food source. A safe food source means they will keep on breeding, and you will never get rid of a flea infestation unless other forms of flea control are used simultaneously. So the flea collar does give you partial protection as long as no fleas enter your home and start breeding, but if they do, the collar becomes useless.
One saving grace does arise from this, though. Because ticks like to attach themselves to hosts' necks, where they are relatively safe from counterattacks, the flea collar can provide some protection from ticks. This is sometimes recommended as an auxiliary measure for dogs that routinely get heavy tick infestations. Unfortunately, ticks are extremely tough creatures, and there is no product of any sort that is proven to prevent ticks 100%. A flea collar or a specifically formulated tick collar may help, but it will not eliminate all tick problems. (Note that even the new topical flea and tick treatments are not 100% effective for ticks).
Another problem with flea collars is that their active agents irritate the skin of a lot of animals, leading to "flea collar dermatitis". This dermatitis is not a serious problem in itself, but animals with skin irritations are prone to scratch the affected area constantly, which can open up a risk of infection.
While we're on the subject, I should point out that the pesticides used in flea collars are species-specific. The agents used in most dog collars are toxic to cats, and highly irritating to humans. (I have to mention this because during both American wars in Iraq, American soldiers have asked relatives to send them flea collars to protect them from sand fleas - an improvised tactic condemned by the Army's Health Services Command as unsafe and ineffective).
Because of their drawbacks, flea collars are an imperfect method of flea control. For a long time, they were the best solution available. But for the the last decade or so we have had a better alternative, in the form of topical treatments such as Frontline and Revolution. These treatments provide total body protection, do not irritate the skin, and can't be torn off like a flea collar. They protect the animal for a month or more, and some of them also protect against heartworm and other parasites. By depriving fleas of a safe food source, they offer complete flea control, with the ability to wipe out a home infestation without using sprays or bombs when used consistently. The major disadvantage of these treatments is their high cost relative to collars, but in the realm of flea control, you get what you pay for.