Every day. Not to whiten my teeth, but because my toothbrush was growing crud between uses. I tried keeping it submerged in alcohol (ethanol) between brushing and though it worked, it tasted awful.
Now I just moisten my toothbrush with Hydrogen Peroxide right before I use it. I don't gargle with it. Read the label, I believe it says it can be used for this purpose.
Hydrogen peroxide is what you give dogs when you want them to barf. Pretty sure this would rule it out as a mouthwash for me!
Cats, too, and it definitely works as advertised that way. But it's necessary to swallow a fair bit of it and normally I spit out my mouthwash. I also might barf if I swallowed an ounce of ordinary Listerine.
My favorite mouthwash hands down is Lavoris, which is hard to find but in the 50's and 60's was very popular. It is red and cinnamon flavored and the ingredients are a very clever formulation, in my opinion scientifically superior to the mainstream mouthwashes that clutter the drug store shelves. (The problem was that nobody believed anything that tasted so good could possibly work as well as things that tasted nasty, or at least that was the marketing spin of the day.)
The main things that create breath odor are amines and sulfur compounds produced by oral bacteria. The cinnamaldehyde and the zinc chloride in Lavoris both react with the amine and sulfur-containing functional groups and make them non-volatile. They also denature any protein floating around and wipe out bacteria. It all goes down the drain. It's always surprised me how many food particles and other junk ends up washing into the sink with Lavoris as compared to the other mouthwashes I've tried.
Some CVS pharmacies may still carry Lavoris, or it can be ordered from drugstore.com. Probably other retail channels, too.
If I knew what I were doing, why would I take lessons?
"Things should be as simple as possible, but no simpler." - Einstein