Family:
Cymbeline (daughter, carried by Remus)
Gaewyn (pet dragon)
The Pup (child, gender unknown, carried by Severus)
Serenus Snape (brother-in-law)
Severus Snape (spouse)
Winslow (pet Criffler)

Pack:
These are those individuals who Remus or Moony recognize on some level as "belonging" to him, as an Alpha Wolf. It is known that Moony would not attack Severus in wolf form, but whether or not Moony would attack Sirius (as opposed to Padfoot) or Bill when in wolf form is not known at this time.
Sirius Black/Padfoot (by Remus and Moony)
Noah Jackson/Khenti (by Remus and Moony)
Severus Snape (as Mate for Moony)
Bill Weasley (as Mate for Khenti, only by Remus)
Remus' former packmates, now deceased, include Peter Pettigrew/Wormtail, and James Potter/Prongs.

Closest Friends:
Hannah Abbott (whom he treats almost like a younger sister)
Sirius Black
Harry Potter
Serenus Snape
Bill Weasley

Lovers:
Sirius Black (once, in adolescence, prior to "The Prank")
Draco Malfoy (once, with a "morning after", located here)
Severus Snape (current relationship, first time located here)
Bill Weasley (once, located here)

Friends:
Remus is friendly with almost everyone he has ever met, so anyone has has interacted with who is not on another list is probably in this category. This includes Order members, most of the Weasley family, and former students (especially the non-Slytherins)

Is Uncomfortable on Some Level With:
Nymphadora Tonks (her one night with Severus and her strained relationship with Bill have served to make Remus feel relatively uncertain of her, even though she was once one of his closest friends)
Blaise Zabini (Blaise's one night with Severus and the now-defunct relationship with Serenus mean that Remus isn't quite certain how to treat Blaise at this point, other than as an acquaintance)

Dislikes:
Percy Weasley

Hates:
Regulus Black
Lucius Malfoy
Kingsley Shacklebolt