There's not really much of a story for me. My dad was from a small town in Montana and moved to the North Bay when he was ten or so - this was in the days of Willie Mays and before the A's left Kansas City, so of course he became a Giants fan. Before that, he had rooted for (shudder) the Yankees. He raised me right, so I became a Giants fan, too.
But I'm curious as to how other folks became fans - especially those of you who aren't from Northern California, don't live here, etc.