I've been checking out a lot of Postmodern Jukebox. They take (somewhat) recent songs and perform them with a throwback style.

Here's their New Orleans Jazz version of Seven Nations Army https://www.youtube.com/watch?v=sB6HY8r983c

And here's their 1920's version of Gangsta's Paradise https://www.youtube.com/watch?v=Rve03u7oEvI