Sacred relationships:
Remus/Moony (Padfoot acknowledges Moony as his Alpha)
Harry (godson, currently housemate)
(James)
(Lily)

Sexual relationships:
(Victor Krum)
Hermione Granger (former relationship; they continue to be friends)
Susan Bones
Percy Weasley
Nymphadora Tonks

One-night stands:
Ginny Weasley

Friends:
All sacred and sexual relationships, plus:
Serenus Snape
Bill Weasley
Noah Jackson (and Khenti) (Padfoot regards Khenti as a junior packmate)

Enemies:
Severus Snape -- Sirius's loathing of Severus is tempered only by his need to not hurt Remus.
Regulus Black -- Mixed feelings would resolve instantly if he knew about the sabotage.
Lucius Malfoy

Other:
Draco Malfoy (housemate, godson's lover)
Molly Weasley (Irritated by, jealous of)
Ron Weasley (Has residual protective and possessive feelings toward)
Ian Scamander (Ian gets under Sirius's skin in the worst way, but Sirius can't beat him up, because of Serenus and Tonks, and he won't avoid him, because that would be cowardly)

Generalizations:
Sirius is friendly to strangers, except when he's not.