I've been aware of Doctor Who since I was a child but I'm not a sci-fi fan in general so I wasn't enthusiastic about it, to say the least. But my friend had been trying to talk me into watching it for some time and when I finally relented and agreed to watch an episode, he wanted it to be the best episode possible. I was hooked as soon as Sally Sparrow found the message under the wallpaper, and now I'm a huge fan. I think he made a great choice!
(Just to be clear, he didn't just dump me in the middle and leave me there. He also showed me Dalek and The Empty Child in order to get me *completely* hooked, then started me back at Rose and from then on I watched in the proper order. This was shortly after the end of series 3 so I watched to that point -- my friend has all of the DVDs -- then started watching old episodes while I waited for series 4. I've now seen series 4 and 5 plus tons of the old episodes. I'll get through all of those eventually too!)
The last fifteen minutes of Stolen Earth. I know, it's weird. My friend was watching it when I went over to her house, and she was watching it because she was really annoyed about not getting to know what happens for a whole week. I was literally stunned by the awesome, and watched The Fires of Pompeii that night.
It's true. She just sat on my couch and watch this supermegafoxyawesomehot man burn. I don't know why she liked it. All she knew was that her friend was watching a show where in 15 minutes a woman could almost get exterminated by a tank covered in balls with a whisk/gun, two people could shoot crazily at another one of these things, and a blond girl could cry over a man burning. Somehow she liked it. If I was in her spot I would have sent her to a mental institution.
Man, it's hard to remember what my absolute first was. It was back in the late 80s/early 90s during a PBS telethon because they were running a marathon of Doctor Who. I want to say it was something with either Tom Baker or Peter Davison as the Doctor, but I can't remember my exact first episode.