Actually, a lot.
If it wasn’t for mythology, our creature selection would be practically non-existent. Mainly we would be going with creatures that actually exist, but probably not Griffons. Also the themes that the creatures represent wouldn’t be included in our stories today.
Not only did we get our creatures from mythology, we also get our archetypes of characters and the concept of quests. From here we take the foundation of the hero, and the fact that he/she must face multiple obstacles to achieve a goal.
As well, mythology and legends were/are the foundation of storytelling, and over the centuries since we have continiously built upon it to create more extravagant stories while still relying upon it’s beginnings.
So, next time you go into the mythology section of a library, bookstore, or website pay close attention, you may find the basic building blocks of your next story there.