My earliest memories of the Internet were visiting my father's house and spending hours on end searching through sites for pictures of folks like Jackie Chan and Jet Li and pictures from their movies, and amassing a big collection of rare photographs. At this time, I intended to create a comprehensive Hong Kong Movie website and I started work on it for my IT AS level at school. When that class collapsed (the school messed it up, along with my AS art class), so too did my drive and I never did do the website.
And yes, all this searching was done using Netscape and AOL.
Of course, the other side of that coin is that I would also spend hours into the night at my dad's looking for porn as well - not videos mind you (they were virtually impossible to find/download) just pictures. At one point, my dad actually had the talk with me too as I probably forgot to delete it all.
For other distant memories (again going way back when), I distinctly remember switching to Google. I had been using Yahoo or Ask Jeeves, but on Dial-Up it was just needless time wasted as Yahoo especially had about a million things on their homepage which slowed it down considerably. In contrast, Google had one modestly sized picture and one search bar and was mercifully quick to load as a result. It wasn't an overnight success (taking years actually) but it still surprises me how fundamentally Google took over.