The Oxford Book of English Verse edited by Christopher Ricks (Oxford, $45). This is the big one, the one where you expect to find everything you half-remember as well as a great deal you don't know. Everything is here, from "Sumer is icumen in" to Seamus Heaney.
The New American Poetry 1945-1960 edited by Donald Allen (Univ. of Calif., $30). This 1960 anthology burst into my life when I was 16 and changed the course of everything for me. Allen Ginsberg's "Howl" was part of it; I had no idea poetry could do anything like that. And Helen Adam, anyone?
Before the Romantics edited by Geoffrey Grigson (Nabu, $33). "Astringent" is the word for this. Not just poetry, but fragments of prose, mostly from the 18th century, cut out by Grigson's hyper-perspicacious scissors.
Palgrave's Golden Treasury edited by Francis Turner Palgrave (Oxford, $25). I still have the pocket-size edition of this collection, which originally was published in 1861. As a child in love with the glamour (the old word for magic) of poetry, I took it everywhere. It's been superseded in many ways, but I include it for the sake of that old love.
The Rattle Bag edited by Seamus Heaney and Ted Hughes (Faber & Faber, $25). The most original, influential, and (most importantly) delightful anthology of the past 35 years. It includes poetry from different oral traditions as well as poetry in translation. It's indispensable.
The Dream of the Poem edited by Peter Cole (Princeton, $20). Sometimes an anthology can open a door into a world whose existence we never suspected. These poems from pre-1492 Spain show us a great civilization and its expression in lyrical, mystical, carnal verse, beautifully chosen and translated.
English and Scottish Ballads edited by Robert Graves (out of print). If you can't find Graves's collection, another one will do. The important thing is to have these great, murderous, ghostly, heroic, unforgettable poems with you in one form or another. "Sir Patrick Spens," for example: No story has ever been better told.