I've heard that adding glycerine (also called glycerol or glycerin) to cakes makes them really moist! is this true?! Has anyone ever tried this?

Yes - it's true for older-style recipe.. You will find it in old British, Australian, Sth African [see a pattern here?] recipes.

Newer/modern recipes with different ingredients and different techniques do not require it.

If you are using a old-style recipe that has it, it is required. Otherwise, don't add it unless you can work out the chemistry of the recipe.