The poems listed here are from various writings of Tolkien.  Although the majority can be found in The Hobbit or LotR, some come from The Tolkien Reader.  Of course, I do plan on adding more in the future.   Note that not all the poems in Tolkien's writings have names.  I have given names to those that were without so as to make a distinction of it.

A
All That is Gold
Aragorn's Song
Athelas
Attercop!

B
Barrels on the River Running
Barrow-wight
The Bath Song
Bregalad's Song
Burn! Burn!

C
Chip the Glasses

D
Drinking Song
Durin's Day

E
Eagles' Song
Earendil the Mariner
Elbereth! Gilthoniel!
Entmarch
Entsong
Eomer's Song
Errantry

F
Far Over the Misty Mountains Cold
Fifteen Birds

G
Galadriel's Message
Gil-galad
The Goblin Song
Goldberry

H
The Hoard

I
The Inn
In Tasarinan
In Western Lands
I Sit Beside the Fire and Think

J

K
The King Returns
The King Under the Mountain

L
Lament for Boromir
Lament for Theoden
Lament of the Rohirrim
Legolas' Song of the Sea
The Lore of Creatures
The Lord of the Rings
Luthien Tinuviel

M
Malbeth the Seer
The Man in the Moon Came Down Too Soon
Merry Dol!  Derry Dol!
The Mewlips
Mound of Mundburg

N
Nimrodel

O
Old Walking Song
Oliphaunt
O! What Are You Doing?

P

Q

R
Return to Rivendell
Roads Go Ever On
Rohan Hymn
Rohirrim Call to Arms

S
Sam's Song in the Tower
Sam's Troll Song
Shadow-Bride
Sing All Ye Joyful
Snowmane's Epitaph
Song of Eldamar
Song of Elves Beyond the Sea
Song of Gondor
Song of Lebennin
Song of Lore

T
Theoden's Burial Song
The Travel Song

U
Upon the Hearth the Fire is Red

V

W
Wandering Through the Old Forest
The Wind Was on the Whithered Heath

X

Y

Z