Maybe more for the younger audience, but there is comic book version of the Finnish epic Kalevala called Koirien Kalevala/Canine Kalevala. Looks like this.

My favorite book on this subject is Myths and Legends, compiled by William Doty and Jake Jackson. It has Celtic, Native American, Chinese, Scottish, Greek, Indian, Norse, and African myths. If you're looking for a broad variety, you can't do any better.

I had an interest in folktales while attending university. A lot of the books that I kept are more specific and adult reader oriented than you're looking for, but I did come across a book called Favorite Folktales From Around the World a few years back, which might fit what you're looking for. It was edited by Jane Yolen, and it's part of the Pantheon Fairy Tale & Folklore Library. The other books in the series also look interesting, though I haven't picked any of them up.

Favorite Folktales has a lovely introduction, where Yolen talks about the traditions associated with oral storytelling around the world. The stories are divided thematically into sections, and each section comes with a brief note of explanation. The tales themselves are simply annotated with the country of origin.

Yolen went for an interesting mix of tales; you won't find any of the stories that have made it into the Disney canon (though you will find variants and antecedents), but you will find a nice representation of stories that are important to cultures around the world, presenting varied and interesting perspectives on life.

The Legends, Myths, and Whiskey podcast might be an excellent place for you to find some more of all the listed above. The hosts are really well spoken, and aren't vulgar. They also provide an incredibly high level of value to the stories with their narration, and custom music made for each story. Definitely give it a listen.