The new Mac App Store can be automatically searched when you click on a file your Mac doesn't recognise. But if you want to see what apps can handle certain extensions yourself, you can do that, too.
Commenter HahSohrob shows us the syntax and provides a screenshot example. Search for
extension:doc, and you'll see all the apps that can handle a Microsoft Word extension. Search
extension:psd for Photoshop files,
extension:zip for compression tools, and so on. It's handy not only for files you're just encountering, but also picking out specific utilities in the store.