The SQL Slammer worm essentially crashed the internet, and that was exploiting a bug that had already been fixed. Imagine if a hacker finds a similar exploit that has not yet been identified and uses it to create a similar worm. You could very easily crash the internet, and not just for a few hours, but for a few days (until Microsoft discovers the exploit and creates a patch and everyone patches their system). It's not too likely, I'll admit, but it could still happen.
Barring that, a sustained DDoS of the root DNS servers could cause some problems, but due to the decentralized nature of the system, ISPs could just stop attempting to look up domain names from the root servers and only websites that change their IPs would be unavailable. At least, I think that's how the system works. Don't quote me.
As for a redesign of TCP/IP, don't count on it anytime soon. The Reg covered something about it
here.