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.

Barrels on the River Running

Roll-roll-roll-roll,
roll-roll-rolling down the hole!
Heave ho! Splash plump!
Down they go, down they bump!

Down the swift dark stream you go
Back to lands you once did know!
Leave the halls and caverns deep,
Leave the northern mountains steep,
Where the forest wide and dim
Stoops in shadow grey and grim!
Float beyond the world of trees
Out into the whispering breeze,
Past the rushes, past the reeds,
Past the marsh’s waving weeds,
Through the mist that riseth white
Up from mere and pool at night!
Follow, follow stars that leap
Up the heavens cold and steep;
Turn when dawn comes over land
Over rapid, Over sand,
South away! And South away!
Seek the sunlight and the day,
Back to pasture, back to mead,
Where the kine and oxen feed!
Back to gardens on the hills
Where the berry swells and fills
Under sunlight, under day!
South away! and South away!
Down the swift dark stream you go
Back to lands you once did know!