Some really good suggestions above. These are ones I haven't seen suggested:
Kanamemo (about a little girl finding a family in friends),
Mitsudomoe (about 3 quirky little triplet sisters getting into trouble)
Is the Order A Rabbit? (about young girls becoming family through friendship)
A Bridge Under Starry Skies (although it seems a bit of a harem at first it isn't really. It's about a group of friends getting closer)
Soul Eater Not (about 3 girls from different walks of life becoming surrogate sisters)
Celestial Method (about a group of friends reuniting after lost friendship)
Kinmoza (about a group of young girls becoming friends despite language/nationality differences)
Read or Die (an adventure involving 3 quirky sisters)
Galilei Donna (an adventure about a broken/dysfunctional family growing back together)
are some of my favorites.
Favorite anime list at http://www.anime-planet.com/users/Reddawnrocker/anime/...