So I have a few I could list, depending on what you're looking for here. If you're looking for "first be news story" I remember it would be Baby Jessica falling down the well.
If we're talking big, huge, national events, I remember the Gulf War starting, but I can't say I remember a specific day or story.
If we're talking about big, huge "the world changed in an instant" type story, then maybe... the Oklahoma City bombing. I think I remember the WTC bombing also, but I only "remembered" it after I was reminded about it recently, if that makes sense? So I don't think that really counts.