GameSpy and the planet network, especially thier hosting / match making systems. Maybe it was just being able to know a couple servers and run into the same people over and over, but I remember liking that a lot.
The Happy Puppy games site.
Not really the web, but the original RealPlayer surfaced some amazing content for the time. I was able to watch Russian news, which while I didn't understand a single word was pretty amazing for a cold war obsessed kid
I suspect the constraints made it better. You’d already dropped a small amount of money on the magazine, built up the anticipation of getting it home, and now you were definitely going to give the demo a good whirl.
Also, demos /shareware were an important marketing mechanism back then, companies took them seriously.