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.

Athelas

When the black breath blows
and death's shadow grows
and all light pass,
come athelas! come athelas!
Life of the dying
In the king's hand lying!