The Big Pitcher
The Big Pitcher was supposedly invented to cure the dreaded problem of Chronic Oxygen Debt Syndrome. If anyone has a fish tank, they pretty much know how The Big Pitcher works. For those who don't, it just blows bubbles up from the stand to the top through the water inside.
The woo-meisters state that the product "polishes" (not filters) customers' water so that oxygen can be absorbed through the mouth since "the GI tract [or lungs it seems] does not absorb gases." This supposedly "hypercharges" blood cells with oxygen and keeps the body's pH at 7.4.
It also contains a very general general patent, which they display prominently on their site like many patent medicines — a patent describing a pitcher with a receptacle for water, air channels to the top, a button, a light, and screen so bugs don't fall in.
The website lists no information saying anything scientific. Instead it has a list of doctors stating that not having enough oxygen in your blood is not good (which is already blatantly obvious) and who mention nothing about drinking it or the potential for absorption through the mouth.
 Chronic Oxygen Debt Syndrome
If it wasn't obvious, CODS is an entirely fictitious disease. The claim is that people are not breathing enough, and there is a severe debt of oxygen in their blood that is the "primary cause of most major illnesses." This is just a pseudoscientific term, based on oxygen therapy woo, intended to scare people into believing they are not as healthy as they should be.
There actually is a book called Oxygen Debt Syndrome: The Physiology and Biochemistry of Living in Oxygen Deficit by Henry F. Peters. There are no references to this author or this text to be found anywhere, including the website for the Big Pitcher.
 What The Big Pitcher Allegedly Helps
Since you are not getting enough oxygen in your blood by breathing, look at all the wonderful things this can help!
- Clumping of blood cells
- Eliminating chemicals and particles in water, even after filtration, while boosting the effects of medications in the blood
- Recovery from illnesses
- Discouraging cancer