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There are currently 4 great noble families, and a series of minor noble families.

The great noble's:

  1. Shihōin Family
  2. Kuchiki Family
  3. Unknown
  4. Unknown
  5. 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):

  1. Fon Family
  2. Kira Family
  3. Kyoraku Family
  4. Ōmaeda Family
  5. Ukitake Family
  6. Kasumioji Family (anime only)
  7. Kannogi Family (anime only)
  8. Ryodoji Family (movie only)

You can find out more at Bleach Wiki.