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.

Song of Elves Beyond the Sea

Ai! laurie lantar lassi surinen,
Yeni unotime ve ramar aldaron!
Yeni ve linte yuldar avanier
mi oromardi lisse-miruvoreva
Andune pella, Vardo tellumar
nu luini yassen tintilar i eleni
omaryo airetari-lirinen.

Si man i yulma nin enquantuva?

An si Tintalle Varda Oiolosseo
ve fanyar maryat Elentari ortane
ar ilye tier undulave lumbule;
ar sindanoriello caita mornie
i falmalinnar imbe met, ar hisie
untupa Calaciryo miri oiale.
Si vanwa na, Romello vanwa, Valimar!

Namarie! Nai hiruvalye Valimar
Nai elye hiruva. Namarie!