I'm not convinced that the internet is going to die. If I'm reading the article right, the problem is that the amount of money that service providers are planning to invest is not enough. Internet service providers are paid by customers to provide them with internet access. That means, if the internet dies, they go out of business. So you'd presume they'd be willing to invest as much money as it takes to keep the internet alive.
I'm not really an expert on these things, but I'd assume that, if there is a true risk of overloading the capacity of the internets, a lot of websites will start deleting old content or put a limit on the amount of content their users can upload. Also, since the service providers are investing more money, I'd expect them to increase their prices for their customers.
It couldn't hurt to get rid of some old internet content, though. If you have any old/unwanted PMs, blog entries, Brickshelf/Maj images, videos or websites that you have uploaded to the internet, II'd urge you to see if you can delete them. I've spent a while clearing out my Maj.