Hmm, most anime I've watched didn't really interest me until the 2nd episode or later... but there are a few that I loved from the beginning.
Fruits Basket:The first anime series I ever watched, (besides the Mysterious cities of gold.) I actually only saw the 2nd half of the first episode over my sisters shoulder, and then rewatched it later the next morning. After that it only took me like a day and half to finish the entire anime with my sister, then we read the manga non stop for like three weeks. Ahh... good times.
Saint Tail: Again, I looked over my lil sisters shoulder, and I was all like, "Hey, whats this???" I sat down next to her and watched the first episode in awe, right after I saw Saint Tail's transformation scene, I was hooked. ^^ I love that show, so much.
And last, but deffinitely not least;
Detective Conan: This show intruged me the most, I had only heard a little about it, and read the review for the dub here. My sister and I started this one when we had a cold earlier this may, the first episode was way different then I had exspected, it was actually really good and had great dialog. I was totally hooked, and now I'm at episode 258. (I love mystery/romances.)
(By the way, watch the sub for ST and DC. They are a zillion times better then the dub.
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Also I'd like to note that all of these shows have exceptionally exellent soundtracks. (That always helps, when the music isn't fitting the scene, it really brings down the value.)