The story in Haibane Renmei starts to develop very (and I mean here VERY) slowly. It seems like each of the first few episodes could be summarised in one sentence. But after some time the patience pays off - the story that initially was hidden starts to reveal itself in a very interesting and beautiful fashion with a culminating point at the very end. Similar situation is present in the case of characters. Initially boring and similar become very interesting and distinct, each with its own story to tell. My personal favourite (and probably of many others) is Reki, who towards the end becomes a new main character of this beautiful anime. Animation and music are both extremely well matched to the story. IMO the soundtrack is one of the best I have listen to in a while.
Maybe this anime is not for everyone, but if you are looking for something more from anime than just pointless action then this seems to be a perfect choice. Highly recommended!