When I'm out for the day, I usually carry a toothbrush with me. If I know that I'm going to lunch with the girls. or family, I take a toothbrush and toothpaste in my purse.
I've learned from experience that toothpaste is not strictly necessary to clean the debris that eating creates. So, when I go hiking and such I don't usually like to waste the weight allocation on things that aren't essential. It's interesting that you mention hiking though, in this context. My hiking buddies spent a lot of time making fun of the fact that I won't carry toothpaste, but I'll carry 2 toothbrushes. One I keep in my hygiene kit which I use when we make camp. The other I keep accessible in my side pouch for when we stop to rest.
Also, I've noticed that I eat less often when I'm hiking. Usually, a cup of water and a dry toothbrush is enough to keep the debris from driving me nuts.