There are currently 4 great noble families, and a series of minor noble families.
The great noble's:
- Shihōin Family
- Kuchiki Family
- Shiba family - Once counted among the great noble families, the Shiba clan fell from favour some time ago.
The lesser noble families include (but are not limited to):
- Fon Family
- Kira Family
- Kyoraku Family
- Ōmaeda Family
- Ukitake Family
- Kasumioji Family (anime only)
- Kannogi Family (anime only)
- Ryodoji Family (movie only)
You can find out more at Bleach Wiki.