While keeping vast amounts of data in your head isn't worth it because of the internet, it is certainly still important to know this stuff off the top of your head.
The more that you keep in your head for later means that you have more information with which to provide a context for other information.
An example: I've been reading Noam Chomsky's book on the Balkans, and I remembered a few things he said. When I saw that Kosovo declared independence via the BBC I had a better understanding of how important that was. This type of stuff doesn't happen when you're sucking info from the internet on demand. When I see some news article, I don't lurk around Wikipedia for an hour researching it, I skip it.
FWIW, knowing is still important. The internet does not replace your brain. It replaces books (kinda).