Usagi Drop. The story of a middle-aged dude whose grandfather passes away, leaving a little girl behind. He takes her in, and little do you know, it becomes a heartwarming slice of life that is so, so very sweet. I heard that the manga screws things up a bit so that things get complicated, but the anime was good. :)
Usagi (or) Bunny Drop! As an anime, it's the quite adorable tale of a nearly middle aged bachelor adopting a little girl who seems to be his recently deceased grandfather's love child. Learning the ins and outs of single parenthood take center stage, and the bond the two develop is heartwarming. NOTE: The manga apparently goes very Shoujo once she's older.