Anime loved and lost would have to be Gundam Wing for me.
It was the first 'serious' anime I watched (dubbed version, I'd never seen anime in Japanese) and I was addicted. I recorded each episode as it aired and rewatched it at least twice over that same day. When I finally had the entire series recorded, I'd spend days watching it over and over till the movie came out, and then I'd watch it all with the movie as cap.
A summer later I was cut off from watching things (working straight through) and when I came back to watch it again...nothing. I really didn't like it. In fact, I started to dislike almost the entire anime except for one or two parts. If I hadn't finally gotten the Japanese version, it would have stayed on my hate list. Watching it in Japanese managed to refresh the entire thing for me, so it's back in my good graces.
Anime that gets better each time? Yu Yu Hakusho. The first time I watched it I was giddy. I'd seen the short 20min movie and that was it. Anyone who's seen that knows it plays more like an episode than a movie so it didn't tell me anything. But I'd read about the anime enough so I had very high expectations. From the first episode those were fulfilled. I fell for each and every character, all the way through. I actually (and I have witnesses

) squeeled like a 15yr old fangirl the first time Hiei used his dragon and I was repeating that line throughout the rest of that episode. I had to pause it for nearly 10 minutes and then go back to catch what I'd missed in my glee. ^_^;; I had the same reaction the first time I saw Kurama shift, and then later on during the other surprises (won't mention those spoilers).
Since that first viewing (2 days - I didn't go to classes or sleep or anything so I could watch it all at once) I rewatched my favorite episodes and recorded my favorite scenes to tape so I wouldn't have to skim through the entire anime to catch them (112 eps is a lot to skim through). I didn't get a chance to actually rewatch the entire anime until a few years later when I had my friend from Indy over. We sat down and watched it all the way through and it was deja vu. I found myself grinning for no reason, just reminded of exactly how much I liked *everyone* and everything in the anime - not just those favorite scenes I'd put on tape to rewatch. It wasn't quite the fangirl reaction I had the first viewing (I managed to grin but not squeel during the great scenes the second time). But it was like I appreciated the other parts even more.
I had the same thing happen with CardCaptor Sakura. I'd seen most of the anime dubbed, but the first time watching the entire thing in Japanese was wonderful. The second time through was much better since I could appreciate everything more, and not get caught up on my favorite parts. I find it's the longer anime with multiple characters that I like best - when they make you like *everyone* without any of those 'love-to-hate' characters. In YYH the closest one was Kuwabara, and I ended up liking him by the 8th episode despite his annoying habits (they became endearing and just fun to watch). In CCS I don't think there is an annoying character for me - I liked them all except Eriol, but even he I can ignore.