If you liked
Kimi ga Nozomu Eien
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...then you might like
Saishuu Heiki Kanojo
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Both Kimi ga Nozomu Eien and Saikano involve the energetic best friend setting up the shy girl with the main character, although she secretly likes the main character herself. Each focus mainly on romance, although Kimi ga Nozomu Eien is more realistic than Saikano. Both shows are extremely dramatic, as well as extremely depressing.
If you liked
Serial Experiments Lain
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...then you might like
Higurashi no Naku Koro ni
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Higurashi no Naku Koro ni and Serial Experiments Lain are both creepy animes that screw with your mind. Each of these animes also have split personalities and weird deaths.
If you liked
Suzumiya Haruhi no Yuuutsu
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...then you might like
Lucky☆Star
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Both Lucky Star and The Melancholy of Haruhi Suzumiya have slice of life school comedy elements to them. Lucky Star has tons of references to The Melancholy of Haruhi Suzumiya, which will be really funny if you've seen the show.
If you liked
Shuffle!
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...then you might like
Kanon (2006)
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Shuffle and Kanon 2006 are both harems with supernatural elements based off visual novels. Shuffle and Kanon 2006 both have five main girls.Many of the characters are similar in personality: Yuuichi-Rin Mai-Primula Makoto-Asa Ayu-Sia Shiori-Nerine Nayuki-Kaede (sort of)
If you liked
Shakugan no Shana
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...then you might like
Suzumiya Haruhi no Yuuutsu
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In The Melancholy of Haruhi Suzumiya and Shakugan no Shana, a normal boy (Yuji and Kyon) is thrown into a completely abnormal world when they meet a girl with special powers (Haruhi and Shana). They both have elements of action, comedy, and romance; with Shana more on the action side and Haruhi Suzumiya more on the comedy side.
If you liked
Fruits Basket
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...then you might like
Vampire Knight
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Both Vampire Knight and Fruits Basket revolve around a girl keeping an important secret. Each are reverse harem, and some of the characters are similar. Yuuki-Tohru Kaname-Yuki Zero-Kyo
If you liked
Lucky☆Star
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...then you might like
K-On!
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K-ON and Lucky Star are both slice of life moe comedies that mainly take place in school. The characters are extremely similar, for example: Konata-Ritsu Tsukasa-Yui Kagami-Mio Miyuki-Tsumugi
If you liked
Fruits Basket
|
...then you might like
Ouran Koukou Host Club
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Fruits Basket and Ouran High School Host Club both are reverse harems that are mainly comedy, but have their serious side too.
If you liked
Air
|
...then you might like
Kanon (2006)
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Air and Kanon 2006 are both based off of visual novels by Key, and each have very moving stories that will probably make you cry. Also, the Makoto and Misuzu arcs are incredibly similar.
If you liked
Death Note
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...then you might like
Code Geass: Hangyaku no Lelouch
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Both Lelouch and Light want to change the world, and obtain a power that allows them to do this: with Lelouch the geass, and Light the Death Note. Lelouch and Light are both insanely smart, as well as manipulative.