Internet Protocol is being upgraded to IPv6 (any decade now), HTTP/2 is replacing the old HTTP 1.x (thanks SPDY!), TLS has replaced SSL, brotli is stepping up for gzip/deflate. Who knows, maybe QUIC[1] will be next.
Even on the programming side we have new languages entering the fray. Javascript has recently gotten huge upgrades, and WebAssembly has a lot of momentum behind it as well.
So on almost all layers we're able to swap in new protocols or technologies and everything still continues to function. It's actually a very robust system when you think about it.
Still, there are a few sore spots. DNS is in need of a redesign in my opinion. It wouldn't be impossible to replace, but not easy either.
A number of concepts in web design (such as "document flow") probably aren't going away either. But newer technologies (canvas, WebGL? who knows) may eventually replace the traditional DOM model.
