Mine was Batman War Games. Tried re-reading it recently and I lost interest and didn't finish it. To be honest I don't remember much apart from Stephanie Brown being killed by Black Mask. Kind of a dud... what was your first event? Is it a classic? A part of me wishes I got into comics around the time of Knightfall or Death of Superman.
My first company wide event was Infinite Crisis but I didn't know what the hell was going on at the time. Reading it years later I really like the book a lot.