I have two. First True Names by Vernor Vinge, published in 1984, which includes the internet in all but name, online avatars and handles, cybercrime and the like.
Then, there is Web of Angels by John M Ford from 1980. A recognizable interstellar internet with hackers, viruses and defense programs.
Followup to my own post. This article indicates that True Names was written in 1979, not 1984 as I stated earlier.
The classic SF novel Ender’s Game, by Orson Scott Card, features a substantial sideplot in which the main character’s two siblings take over the world by posting political essays on the “nets” and participating in online debates, in a manner nearly identical to modern-day online message boards and political blogs. The primary difference is that the nets of Ender’s time seem to be more centralized, with government-run accounts. There is also a higher guarantee of anonymity, as only officials of the world government are capable of discovering the identity of a demagogue who wishes to remain anonymous (and it is implied that, even then, it’s frowned upon as a violation of privacy).
In his later books, Card incorporates more aspects of the real internet, to the point that the current incarnation of the nets as described in the latest “Shadow” novels is clearly intended to be a futuristic successor to the internet of today.