This is part of the "whatnot", I guess. :)
There is a whole lot that requires at kende. Generally, kende is used for things you're familiar with, and vide with facts, but I'd expand that a bit: use kende with nouns as the object: "Jeg kender svaret" - "I know the answer"; "Kender du tallene?" - "Do you know the numbers?"; "Vi kender denne historie" - "We know this story."
With vide on the other hand, there is most often a clause following: "Jeg ved, hvordan hun hedder" - "I know how she is called"; "Ved du, hvor mange mennesker var der?" - "Do you know how many people were there?"; "Vi ved at du gerne vil fortælle det." - "We know that you want to tell about it."