Disclaimer: As I said, this is really weird. It might make slightly more sense if you've read Daybreak in Valinor, but only slightly.
Gil-galad was beautiful even by elf-standards, and many of the maidens in Lindon were in love with him, but he never married. For this reason it became a popular Elvish drinking game to sing about how all the prominent personalities of the time as well as the heroes of old and the Valar themselves were hopelessly in love with Gil-galad. After the death of Gil-galad, this custom died out; it was considered bad taste, especially the verse about Celebrimbor. However, it was later revived on Tol Eressëa.
The first two verses were always the same. After that everyone took turns to sing, and those who could not come up with a verse had to drink. The verses were originally improvised, but it was not against the rules to use verses someone else had invented. Indeed, some of the verses became classics and were sung almost every time the game was played.
If you think this sounds implausibly hard, you must remember that elves do not get drunk easily, so they need harder drinking games. Also keep in mind that they have excellent memories. I would not recommend humans to play this. However, if for some reason you do end up playing this, don't make up a verse about Eru Ilúvatar, because the rules state that then you have to drink the entire bottle.
These are all the verses I've heard (well, all the verses I've heard and remembered), but there are probably many I haven't heard. There was a certain tendency for the verses to become more... imperfect as the night went on, so don't expect all of these to be flawless.
Gil-galad is an elven-king
of whom the harpers gladly sing.
All maidens seek to be his wife
but he prefers a lonely life.
He breaks the hearts of men and elves;
they look at him and lose themselves
deep in his fiercely shining eyes,
but none can melt his heart of ice.
The blue eyes of the Lord of Breath
no longer look at Elbereth;
on Gil-galad alone they gaze
enchanted by his wondrous face.
Two wives the High King Finwë had,
but now they both want Gil-galad;
fair Indis and proud Míriel
to Finwë king have said farewell.
Turgon, whose wife was lost at sea,
he would no longer grieving be
if he could see Ereinion;
then soon his past love would be gone!
If Húrin on Thangorodrim
faced Gil-galad, he'd yield to him;
against the Dark he could persist,
but Gil-galad he can't resist.
Pale Estë can no longer rest
until her love she has expressed.
"Sweet Gil-galad," she says, "be mine!
For you I long, for you I pine!"
Celebrimbor forged a ring
and gave it to the elven-king.
As surely as stars shine above:
to give a ring is sign of love!
Many secrets Ulmo keeps
in his mansion in the deeps,
but the greatest of them is
that Gil-galad he wants to kiss.
Morgoth cries outside the world,
wailing without being heard;
Gil-galad's enchanting charm
makes him wish he'd done no harm.
In Lórien does Irmo weep
and finds no comfort in his sleep;
no dream of Gil-galad can be
as lovely as reality.
And in the somber halls of doom
Námo's heart is filled with gloom.
He suspects he's going mad
out of love for Gil-galad.
Vairë's crying as she weaves
and we all know why she grieves;
though she hides it, we can tell
she loves Gil-galad as well.
And Tilion no longer tries
to catch the sun, for now his eyes
and fixed on Gil-galad the fair;
moonbeams he sends to stroke his hair.
The second son of Fëanor,
who wandered sadly by the shore,
threw one glance at the elven-king;
of love he then began to sing.
Why, even Fëanor himself
is charmed by this enchanting elf;
a Silmaril he'd gladly give
if he with Gil-galad could live.
Tulkas used to laugh all day
but now he's filled with great dismay.
After all the fights he's won
he lost his heart to Ereinion.
Beren fell for Lúthien
when he saw her in the glen.
If he'd seen Gil-galad instead,
then Lúthien would not be dead.
Uinen, lady of the seas,
can no longer be at peace;
her white arms, her flowing hair
can't the elven-king ensnare.
Amarië, she waited long,
but now she's tired of being strong:
"Finrod, try not to be too sad;
I'm leaving you for Gil-galad!"
"Never once was given birth,"
says Yavanna, queen of earth,
"to a beauty equal to
Gil-galad - I swear it's true!"
Nor did Aulë ever wring
- he admits it - anything
that could match Gil-galad's grace
and the splendour of his face.
Eärendil, who sails the sky,
saw Gil-galad, and had to cry;
for he was bound to sail above
and could not meet his newfound love.
Even the wise Galadriel,
though married, fell under his spell.
With Celeborn this caused no strife:
he was as smitten as his wife!
The faithful Morwen Eledhwen,
the fairest daughter born to Men,
less faithful would perhaps have been
if Gil-galad she once had seen.
Elrond could choose for himself
whether to be man or elf -
but as a man, he could not be
with Gil-galad eternally.
Now Fingolfin and Finarfin
are fighting, for they wish to win
the heart of our Ereinion;
they both love him, but he loves none.
Arien was once her name,
the sun-maid clad in living flame,
but the name she wishes she had
is that of 'wife of Gil-galad'.
Thingol, who heard the nightingales
of Melian, would say she pales
besides the beauty of the king:
of him the nightingales should sing!
Never did Oromë catch
any being that could match
Gil-galad in loveliness
and this causes him distress.
Yes, even Varda Everwhite
says Gil-galad shines twice as bright
as any star forged by her hand;
such beauty she cannot withstand.
If Lúthien had seen hís face
she would not seek a man's embrace.
And Idril, too, would change her choice
if she had heard Gil-galad's voice.
Tears always filled Nienna's eyes,
but now it's for herself she cries,
for Gil-galad she wants to wed,
but he prefers his lonely bed.
Turambar Húrinion
Agarwaen Úmarthion
Mormegil Adanedhel
Túrin would love the king as well.
Sweet Vána in her gardens fair
is filled with sorrow and despair;
she wants Gil-galad for herself,
but she can't charm that stubborn elf.
Ossë rages in the sea
- and what can the reason be?
Why, it's love for Gil-galad
that has made him go so mad.
Upon the grass of Valinor
the feet of Nessa dance no more.
She too has fallen for the king
and no more joy does dancing bring.
Both Celegorm and Curufin
and Amrod and his fated twin,
and Maedhros and Caranthir, too -
all want Ereinion for their beau.