If you're looking for anime similar to Ar Tonelico Sekai no Owari de Utai Tsuzukeru Shoujo, you might like these titles. All recommendations are made by Anime-Planet users like you!
As an orphan whose life is in the hands of space pirates, Coud has had no choice but to survive on bravado alone. He has nothing to live for until he finds Ren entombed amongst the treasures in the pirate ship's hold, and awakens her. In addition to being mysterious and beautiful, Ren can transform into a battle sword to help Coud fight and prove his strength -- but with this strength comes the bitter realization that power alone is not enough. Now, in a race against time, Coud must endure betrayals and fierce battles as he struggles to return Ren to her home, before it's too late...
Both anime follow the story of a young and careless boy who pair up with a girl with magical power. Songs play an important role in both, being the way magic is activated. Both also take places in a fantasy world filled with monsters and advanced technology. Also, the relationship between the main characters is a focal point in these two series. And lastly, both are quite funny.
However, keep in mind that Ar Tonelico is only an OVA which serves as a presentation of a videogame (and thus its plot is extremely simple). The game has even more in common with Elemental Gelade, but that's another story. Anyway, if you liked one, I'm sure you'll like the other!
Both series revolve around young girls who fight using the power of songs and as expected they both have fantastic soundtracks. Story wise the two shows aren't really similar due to Ar Tonelico being a single OVA based off of an RPG but fans of the OVA/game should check out Symphogear; while Symphogear fans should test out AT's ova and possibly move onto the original game as both series carry the same theme that any conflict can be solved with words alone.