Tomoya Okazaki is a third-year high school student who is generally bored with life and doesn't take his studies, future, or anything else seriously. One day, however, he meets a lonely-looking girl in the school courtyard, Nagisa Furukawa. She explains to him the source of her loneliness: she had missed a lot of the previous school year and thus is repeating her third year; everybody that she knew has already graduated, and she is lonely. Tomoya is rather indifferent at first, but decides that he has nothing better to do and spends increasingly more time helping Nagisa restore the school drama club. As his relationship with Nagisa grows, Tomoya begins to open up to various other people around the school as well...
What makes each of these shows special is the depth of the relationships between the characters. Unlike many school romances, these shows take things one step further and show that everything isn't always perfect, that friendship and love involve trials, and not everyone always gets what they want. There is something deeper in these shows that you don't see in a lot of animes. They really explore the human heart and all it's levels and leave you feeling happy and sad at the same time. There is a supernatural element to each show that is vital to the plot. There's not a lot of anime out there that does what these shows do, and if you liked one I'm sure you'll like the other.
Natsume is lonely; he has an ability that separates him from others: he can see and interact with spirits. Soon, however, Natsume discovers that he’s not alone: his grandmother Reiko also had the gift. But things get hectic and possibly dangerous for Natsume when he finds out that he also inherited the 'Book of Friends', a book that contains the names of all the spirits Reiko defeated and subjugated. He finds himself hounded by his grandmother's underlings and, with the help of a 'cat' charm spirit, decides to free them from the Book's shackles, as well as protect the book from those who seek to misuse its power...
Both of animes have at lease some paranormal aspects. Clannad has a slight dose of it, while you can say natsume is a full meal. They both have a nice slow pace that doesn't really become annoying. And the bigest similarity in both of these shows is the warm fuzzy feeling they leave at the end of the episodes.
Once there lived an eccentric author called Drosselmeyer who wrote grand tragedies - one of them was the tale of a prince who sealed away an evil raven by breaking his own heart into tiny pieces. However, before the story could be completed, the author died and the tale took on a life of its own. Now, in a town where fiction and reality meet, the story continues on its tragic course with Ahiru, a duck who transforms into the beautiful Princess Tutu in order to restore the prince's heart. But will Ahiru's act of love be enough to defy the story's terrible destiny and lead to a happy ending?
On the surface, these are two very different shows, and in a way they are. That being said, both are cute, funny stories in the beginning that end up being sometimes happy, sometimes sad, but always heartwarming and moving. Both series have some really gorgeous animation as well (although I think clannad had a higher budget and it shows) and great soundtracks (Tutu even has classical music throughout). Other similar elements are a strong focus on character development, and a similar relationship between the two leads in each show. If you're a Clannad fan, don't let the weird plot of Tutu throw you off, it's wonderfully written. And if you're a fan of Tutu, don't let yourself be fooled into thinking this is just another VN harem anime--there's much more to this series than "which one will Tomoya end up with?" Both of these are firmly on my list of favorite anime.
Ayato Kamina may seem like an average boy in a devastated world, but after being captured by TERRA, a military organization set on saving the world from the Mu, an alien race set on "tuning" the world, he realizes he is an instrument in deciding the fate of humanity and piloting RahXephon. Not only is Ayato the only person who can control the mecha, but he also has a terrible fate of his own. Holding onto memories of his old life and grasping to keep his own humanity, he must struggle in this new world and realize his true potential with RahXephon.
This is more of an absract recommendation. If you liked/disliked the meccha/action part of Rahxephon or the absence of it in clannad then it may not be for you.
This is for the music. Both have a certain emphasis on music (moreso in Rahxephon) and the creators put in alot of effort to make amazing soundtracks.
Also, the major characters love stories are both...special. Without spoilers, I can't really explain why, but the main characters love plots are just...touching.