Eureka Seven - The entire second half of the series. The first half is good too, but it really picks up on the second half. The relationship between Eureka and Renton evolves into a very touching dramatic escapade, as well as the acting gets more gruesome and emotionally intense. Most notable moments without ruining everything would be, whenever Holland does something crazy (like jump out of an LFO into his own), when Renton realizes that he's been killing people, the entire Ray and Charles sequence of events, and the ending. Man, I love that show.

Scrapped Princess - Nearing the end when Pacifica (SPOILER)loses her memory.

Kimi ga Nozomu Eien - All of it. This anime will make you cry.

I just want to note that there are a ton of excellent anime out there that I've seen but I cannot remember specific details to. Animes such as Fullmetal Alchemist, Last Exile, Onegai Teacher, and Basilisk. I remember them all being really good. The three that I've listed doesn't signify the best of the anime I've seen, but rather details I can remember.