I am surprised no one posted here yet... Guess I'll kick it off then!
I present to you the "Markirya" - the single longest piece of mature Quenya text, this poem was published as an addition to the essay A Secret Vice in the collection The Monsters and the Critics (1983). This is the latest, most final version of this poem. The English translation was reconstituted by Édouard Kloczko after Tolkien's translation of earlier versions of the poem and the vocabulary of the glossary added to the essay.

Man cenuva fána cirya
métima hrestallo círa,
i fairi néce
ringa súmaryasse
ve maiwi yaimie?

Man tiruva fána cirya,
wilwarin wilwa,
ear-celumessen
rámainen elvie
ear falastala,
winga hlápula
rámar sisílala,
cále fifírula?

Man hlaruva rávea súre
ve tauri lillassie,
ninqui carcar yarra
isilme ilcalasse,
isilme pícalasse,
isilme lantalasse
ve loicolícuma;
raumo nurrua,
undume rúma?

Man cenuva lumbor ahosta
Menel acúna
ruxal’ ambonnar,
ear amortala,
undume hácala,
enwina lúme
elenillor pella
talta-taltala
atalantea mindonnar?

Man tiruva rácina cirya
ondolisse morne
nu fanyare rúcina,
anar púrea tihta
axor ilcalannar
métim’ auresse?

Man cenuva métim’ andúne?

~~~

Who shall see a white ship
from the final beach steering,
the vague phantoms
in her cold bosom
like gulls wailing?

Who shall heed a white ship
like a butterfly fluttering,
in the flowing sea
on star-like wings,
the sea foaming,
the foam flying in the wind,
the wings shining white,
the light slowly fading?

Who shall hear the roaring wind
like the many leaves of the forests,
the white rocks growling
in the gleaming moonlight,
in the dwindling moonlight,
in the falling moonlight
like a corpse-candle;
the storm grumble,
the abyss move?

Who shall see the clouds assemble,
the Heavens bending
upon crumbling hills,
the sea heaving,
the abyss yawning,
the old darkness
from beyond the stars
sliding down and collapsing
upon lofty ruined towers?

Who shall heed a broken ship
on the many black rocks
under shattered skies,
a discoloured sun blinking
on bones gleaming
in the last down?

Who shall see the last evening?

Probably my favorite poem from Middle-Earth. I won a poem competition with it, and I love the melody Howard Shore put to it in the movies, though the minor key does sound weird in some of the verses.

Upon the hearth the fire is red,
Beneath the roof there is a bed;
But not yet weary are our feet,
Still round the corner we may meet
A sudden tree or standing stone
That none have seen but we alone.
Tree and flower and leaf and grass,
Let them pass! Let them pass!
Hill and water under sky,
Pass them by! Pass them by!

Still around the corner there may wait
A new road or a secret gate,
And though we pass them by today,
Tomorrow we may come this way
And take the hidden paths that run
Towards the Moon or to the Sun.
Apple, thorn, and nut and sloe
Let them go! Let them go!
Sand and stone and pool and dell,
Fare you well! Fare you well!

Home is behind, the world ahead,
And there are many paths to tread
Through shadows to the edge of night,
Until the stars are all alight.
Then world behind and home ahead,
We'll wander back to home and bed.
Mist and twilight, cloud and shade,
Away shall fade! Away shall fade!
Fire and lamp, and meat and bread,
And then to bed! And then to bed!

I have a couple of favourites, but the main one is probably the Lament for the Rohirrim. It expresses, a lot of Tolkiens works, a great sorrow about the passing of time and the decline of all things magnificent with it.

Where now the horse and the rider?
Where is the horn that was blowing?
Where is the helm and the haueberk
and the bright hair flowing?
Where is the hand on the harpstring
and the red fire glowing?
Where is the spring and the harvest
and the tall corn growing?
They have passed like rain on the mountains,
like the wind in the meadow.
The days have gone down in the West
behind the hills, into shadow.
Who shall gather the smoke
of the dead wood burning,
or behold the flowing years
from the sea returning.

This poem here is one of my favourites and a beautiful construct showcasing Tolkien's talent to his limit:

Spoiler

Hey dol! merry dol! ring a dong dillo!
Ring a dong! hop along! Fal lal the willow!
Tom Bom, jolly Tom, Tom Bombadillo!

You did a great job.