The website of the Academy of American Poets provides some suggested poems appropriate for funerals. Recommended elegiac poems include "Because I Could Not Stop for Death" by Emily Dickinson, "In Memoriam" by Lord Alfred Tennyson and "Funeral Blues" by W.H. Auden, among others. Links are provided to each poem.
Additionally, the website of the Poetry Foundation, which publishes Poetry Magazine, includes a searchable database of poems with life events such as death or sorrow and grieving available as limiting options. Users may select as an option only poems which have been published in Poetry magazine; this provides a more contemporary set of poems than the more traditional options suggested by the academy.
Those who are commemorating a lost loved one may also wish to consider not just elegiac poetry but also poems that celebrate the loved one's passions. Poems celebrating nature or family, for example, may be found on both of the websites mentioned above. Song lyrics, themselves a type of poetry, could also be used in place of formal poetry. Especially if the loved one had a favorite band or singer, reading a song can be a way to honor him. Sites such as MusixMatch.com allow users to search for song lyrics by title, artist or lyric.