I started off watching Sailormoon in 1996 when I was 13. It was on at six in the morning back then, and one day I was watching TV a bit earlier (staying up all night, basically

) and at 5 or 5:30 I caught an episode Dragonball (I think it was the episode where they met Oolong or something). I thought it was kinda cool, but I kind of forgot about it.
Then a couple years later, I started catching DBZ when it was playing in syndication on Saturday mornings. I first saw parts of the Freeza saga (around the time shortly before Dodoria and Zarbon were disposed of, I believe), and I became really interested in it and started watching every week. What sucked was that they kept looping the same episodes over and over, but they didn't even start over from the beginning. They just started from a point where Gohan and the others were already on their way to Namek, played until the end of the second season, played the edited version of movie 3, and started over from that same point in the Freeza saga. Even though I had no idea why Vegeta called Gokuu "Kakarrot", I still thought he was cool and badass back then and he quickly became my favorite DBZ character (to this day, he's still my favorite anime character).
After awhile, they stopped showing them on Saturday mornings and I didn't see it for awhile. Then, I guess it was 1999 (whenever season 3 started playing) when I started getting Cartoon Network and one day I was watching and saw commercials for DBZ. I started watching and was pleased to see Gokuu fighting Freeza. I had seen the same buildup episodes over and over before, and now I was finally seeing the payoff. I was especially pleased that after they finished the Freeza saga, they started over at the Saiyan saga, so I finally got to see how it all started! Oh, joy.
As for the Japanese version, my first exposure came in maybe 2000 or 2001 when I started getting the International Channel. They were at the point in the Cell Saga where Gokuu and Gohan were training for the Cell Games. I was a little put off by Gokuu's voice at first (I kept thinking he sounded like a teenage girl

), but I got used to it ^_^ I soon started getting fansubs (HORRIBLE quality >_<), but eventually began collecting the DVDs, and now I have an assload.