Gigamesh is a beloved being to those he held dear.
Shamhat was a good friend of Gilgamesh as well, back before Heaven conquered their World. She seems to have betrayed him in the past, but Gilgamesh had forgiven her (citing, "in love all is forgiven").
Dantalion and Gilgamesh have know each other for a long time. Dantalion had not considered Gilgamesh a friend, treating him more as an annoyance.
Gigamesh calls Dantalion his friend, and has dragged the latter to: an upper-class Demon's Scotch Club, the hot springs of the unexplored world, the New World where they were covered in fluffy fur and to being a servant to the cats, over the years.
Gilgamesh is good friends with Samael, however interaction between them hasn't been shown.
Sytry and Gilgamesh seem to know each other. Sytry is wary of Gilgamesh. And Gilgamesh doesn't seem to care about the former at all, callously offering to kill him to Dantalion. 
Camio and Gilgamesh have been shown to know each other, the extent of their acquaintance is not clear.
Camio seems apprehensive of Gilgamesh. 
They haven't interacted much, but there is some animosity between the two.
Gilgamesh had been an ally of Michael back in the distant past. He seems to have been an valued ally to Heaven, as Michael seemed shocked when Gilgamesh betrayed them. Gilgamesh didn't seem to hold any esteem towards Michael and the Angels and easily turned on them.