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.

Sing All Ye Joyful

Sing all ye joyful, now sing all together!
The wind's in the tree-top, the wind's in the heather;
The stars are in blossom, the moon is in flower,
And bright are the windows of Night in her tower.

Dance all ye joyful, now dance all together!
Soft is the grass, and let foot be like feather!
The river is silver, the shadows are fleeting;
Merry is May-time, and merry our meeting.

Sing we now softly, and dreams let us weave him!
Wind him in slumber and there let us leave him!
The wanderer sleepeth. Now soft be his pillow!
Lullaby! Lullaby! Alder and Willow!
Sigh no more Pine, till the wind of the morn!
Fall Moon! Dark be the land!
Hush! Hush! Oak, Ash, and Thorn!
Hushed be all water, till dawn is at hand!