I've been experimenting with natural stuff with no additives. This home made tooth powder/paste contains xylitol, bicarbonate of soda and slippery elm but you can also add neem, peppermint or clove oil to flavour it and and glycerine to make it into more of a paste.
For anyone worried about fluoride and/or SLS in their commercially made toothpaste.
Another, slightly surprising ingredient you can add (that I didn't mention in the video) is turmeric to whiten your teeth. It sounds like it would never work, but in fact if you rinse your mouth well afterwards it makes your teeth look shining and bright (though your tongue is likely to be rather yellow, so be aware).