What a gloriously open ended question!
Well, universal gigabit access for a start with much greater coverage. This will help to bring in new services that aren't possible now and may not even have been imagined. The speed continues to get ramped up past that over time, too.
Further out, perhaps neural links to the internet. Effectively, the smartphone will be in your head with functionality that's sci-fi right now. I can see this being very expensive and controversial though.
I can just imagine the Apple Faithful going into the Apple store for their neural implant.
A blissful, slightly zombified smile appears on their faces as it goes in, which remains there. They then walk out in a slow, measured way (still with smile) their bank accounts suitably drained and now fully controlled by their Apple Overlord, their one mission to get everyone else implanted too. Now, just who wouldn't want that?!
Just imagine how dated and quaint today's smartphones will look compared to that.
Oh, and of course, everyone on the planet to sign up to NerdZone and start posting fervently!
Might put a little strain on the infrastructure...