I want to start by reminding everyone to be aware of the many sls-free toothpastes that are also flouride free. This may not be what you are looking for if you are into cavity prevention. The only times I have ever gotten cavities in my life is when I used flouride-free, sls-free toothpaste. So maybe flouride and sls are both considered poisonous to some people who also demand that all of their products be made by solar power. However, I find that one of the points of brushing my teeth is to NOT get cavities while at the same time NOT dying from an allergic reaction.
UPDATE! As of March 2018 the original Closys now contains a coconut derived ingredient!

Water (Aqua), Calcium Carbonate, Glycerin, Magnesium Aluminum Silicate, Alcohol, Flavor (Aroma)*, Krameria Triandra (Ratanhia) Root Extract, Commiphora Myrrha Resin (Myrrh Resin) Extract, Xanthan Gum, Ammonium Glycyrrhizate, Limonene*.
* from natural essential oils
NO LONGER AVAILABLE:
Tom's of Maine used to have such awesome toothpastes that they have now taken off the market. They have only kept their flouride-free sls free ones, but sls-free does NOT mean coconut free in these new pastes, unfortunately. Booo!
Original Closys now contains "sodium lauroyl sarcosinate"!
Please comment with your favorite toothpaste! Or invent your own so that we don't have to spend a fortune on this stuff.