Knowledge is not obsolete. It creates a human connection when we know the same things in our heads instead of having to look them up. Imagine trying to get in with a new crowd, but you have to look up their inside jokes on the internet every time they're told. You'll be the one laughing five minutes after everyone else stops, by which time you've missed everything else. You need that social bonding and shared culture information in your head. Your brain is faster than the internet, and it's the only thing fast enough for social interaction. What's more, this is always going to be true. Even if you had something like Google Glass looking it up for you automatically, trying to push answers back at you in real time, there would still be a delay.
Also, there are some things that you won't know how to look up, no matter your search skills. What kind of maths to apply to a certain situation is one example that springs to mind. If you don't know that Return on Investment is a form of simultaneous equation situation and know how to solve them, how long is it going to take you to look that up and learn how to do that maths?
Lastly, sometimes search just fails. If someone uses the wrong term for something, or misuses an existing term, your search will be off the rails before you begin unless you know how to correct it. Or if you're searching for something obscure that is overshadowed by something much more popular with a similar name, like Michael Bolton the computer programmer for Initech rather than Michael Bolton the musician. Lots of obscure things are, well, obscured by mainstream things online, just because they are named the same or similar to each other.
Mokalus of Borg
PS - I wouldn't say I hold a lot of useful stuff in my head.
PPS - This post inspired by this TED talk.