Kanon

Both series have excelent graphics, a cute romance storyline and unexpected (yet captivating) phenomena. Also the episodes' opening story/narration is cool. 

Beautiful Story, too much story about characters, beautiful, moe and kawaii characters. 

Elfen Lied and Kanon?... really?... is probably what your thinking but I'll say from my experience with anime, Kanon is the closest thing I've found to Elfen Lied. Both stories investigate the past as a character returns to a memorable town of their childhood and they begin to live with their cousin. From there both stories explore the concept of memory loss as forgotten/repressed memories begin to resurface. Lastly both anime contain romance and supernatural elements. Elfen Lied differs being a psychological horror with some action, nudity and gore. While Kanon is more focused on drama, slice of life and tragedy. So, if your a fan of a story that investigates a characters forgotten past with elements of romance and the supernatural, I suggest you check out these series. read more 

A guy moves to an other town and meets lots of girls Female characters are very similar Protagonist characteristics are the same  

Both based on visuals novels by Key, one guy helps out lots of girls with their problems. Supernatural theme 

They both involve similar animation and depp plots that make you wanna cry at the end but then end with a smile. they both are the deepest anime i have ever seen and teach you how to be a better person while giving you the entertainment of a extremely well written romance, comedy, drama. 

Some similar story like some guy came back to its home town to find its childhood friends and they start remembering their pasts. 

Both series contain romance as one of the main themes but in a more mature way the typical "love-dovey" scenes. In both series, the drama is quite realistic and serious that also has psychological and emotional tones occasionally. Both series also contain tragedy themes involving love triangles, misunderstandings, and hardships. But there is also some comedy and the characters are appealing as episodes progresses to see the way they change as they adjust themselves and realism of life.