When did the web stop feeling explorable?

Search is useful when you know the question. Feeds are useful when you want more of what already held your attention. But I miss opening a browser without knowing where I would end up.

That frustration became Web Wander, but I am curious about the broader memory: what made the web feel genuinely explorable to you?

Was it webrings, StumbleUpon, random-site buttons, personal homepages, RSS, old forums—or something else entirely? What would you bring back, and what should stay buried?