I know I can get it on Amazon for mere pennies, but it's a matter of getting off my lazy butt and ordering it.
Anyway, another show I like that doesn't need any introduction to anyone here, but I feel like talking about my first experience watching it, is Doctor Who.
The very first time I tried to watch it was during the season 1 episode, Dalek; I came in half-way through the episode, and because I didn't know anything about the series prior to some crappy promos on BBC America (Which literally amounted to "Doctor Who: coming soon..." while showing little to no clips from the show), I was left wondering "What the hell is going on?". However, I gave the series a 2nd chance in late summer '08; after reading up on it out of curiosity and then coming in at the start of the season 3 episode, Human Nature. From that point on, I was hooked on the show; going back and watching some of the original series while following the new one, and before I knew it, I had seen every single episode from '89 to present, as well as all the Dalek episodes from Genesis on up to the most recent one.
Since this will likely come up since I brought up Doctor Who, my favorite incarnation of the Doctor would have to be the 7th. He was definitely interesting; he seems goofy on the outside, but inside he was a cunning mastermind who saw the struggle between good and evil as being like a game of chess.