It's new, but it's fast becoming the primary way the people consume content with: Internet news, video streaming, social media, music libraries in the cloud, etc. I think it's likely to stay as long as there's electricity available. As for censorship, it's inevitable.

Considering it is rapidly growing and expanding, it may not be exactly what we consider "the internet" in 20 years, but it will still be around in the same way the early BBS systems evolved into the forums we have now.
It may be slightly less open though.

The internet will probably be around for a long time to come but its importance will diminish greatly, probably in a decade or two, when it is displaced by some superior and inevitable technological advancement that we can't begin to imagine at this time.

Indeed. I can remember a time when it seemed that vinyl records would be the only thing forever and EVERYONE had a massive collection of them. Or there were just three commercial channels on TV and VCRs were unimaginable. All TVs were black and white and used tubes so they had to warm up before they came on. Everyone had just one phone, it was black, had a rotary dialer, and it sat in one spot forever. No one even had answering machines. If you wanted to record any type of sound at all it was via a big reel to reel tape recorder. Home video cameras were huge,  clunky things that also uses reels of film. You needed a separate projector to view the films. You had to show them on a big portable screen that everyone had. Unless you spent a fortune for very expensive Polaroid film you had to send all of your camera pictures away to be developed. There were NO computers, home or otherwise, and no such things as video games. There was no satellite communication because there were NO satellites.  I could go on. The rate of technological advancement keeps snowballing. I keep waiting for it to level off but that hasn't happened. I agree with c_a. Amazing things are just on the horizon.