I've watched so many as I'm sure many of you have so I'll go more recent. High School DxD and Haganai are both really good and a little different from the norm of the genre.
School days O.O!? I was surprised that you wrote that xDD
But I don't have that many, because I have almost just started watching anime, but some of my favorites are:
Clannad
Kanon
Kimi ga nozomu eien (Rumbling hearts)
Air
Sword Art Online (Its something new, and so far its great It has abit of romance in it aswell)
Chobits
To Love-Ru (harem -.- )
Da Capo, Da Capo SC
Da Capo II, Da Capo II SC
Seto no Hanayome
these are some, plenty to come:P
This http://youtu.be/EtCQB5LQRKM ahahahhahaahh xDDDD!!
Clannad: After Story is probably the best just because it takes the basic principles of the Romantic genre and takes issues that are not usually shown or talked about in Anime and makes it very touching. The best by far when it comes to real life issues, there needs to be more like that.
Most interesting ever would probably have to be: ef - a tale of memories
Characters were great, the mixed intertwined stories were done well, and the story between Renji and Chichiro was different because of her memory lose and how she wouldn't even remember him the next day if it wasn't for her dairy. Very Interesting.
Rumbling Hearts was really good it is one of the few anime I have re-watched completely. Suzuka is good too and I really loved Kimi no Todoke... which is the sweetest story I have ever watched. Ano Natsu de Matteru has alien love! It is really sweet. But Clannad is easily the most epic for me even though I kept waiting to see more action... in terms of development over the season and getting attached to the characters, Clannad achieved that the best but it also comes at a price.... it was soo slow moving.