The first time I heard of Delphi was sometime during the beta. There was this article (or maybe a flyer) talking about "Delphi 95". I'm not sure if that "Delphi 95" term was made up locally by the Swedish reseller DataBiten, or if it was used by Borland locally or globally. I don't think I've seen "Delphi 95" in any other article.
Anyway, I was evaluating dBase for Windows (actually, the beta of it - BladeRunner), and here comes this flyer. It was talking about database and client/server stuff. Very cool. Gotta get it. And we did. This "Delphi 95" beta thing kicked some serious [...] on my projects... :p
Later on, I talked people into letting me go to BorCon in San Diego in August of 1995, and met cool people like Steve Teixeira, Nick Hodges, et al.
Shortly after coming back from BorCon I was offered a job in Delphi Developer Support. It took about six months to get all the visa stuff done, and I started at Borland International on March 25th, 1996. And the rest is history!
Happy birthday Delphi! Only eight more years, and you're a full-grown adult! :p