Forget the green beer. After having discovered genuine Irish ancestors in my heritage, I'm even more convinced that any good celebration of St. Patrick's Day must include singing his very own hymn, usually called St. Patrick's Breastplate or I Bind unto Myself Today. The words are attributed to St. Patrick himself, with the modern, metrical version provided by Cecil Frances Alexander.
The challenge in St. Patrick's for first time singers is finding the flow; the first verse is shorter than the rest, one or two verses (depending on the version) are sung to a different tune, and usually you must turn the page to complete this hymn. (In my favorite hymnal it covers four pages!)
The tunes are Irish and easily singable, however, and the words packed with theology, beauty, and joy. Do yourself and St. Patrick a favor, and honor him on this day by becoming acquainted with this grand and glorious expression of ancient Celtic Christian faith.
The Oremus Hymnal includes the commonly sung verses and page numbers for St. Patrick's Breastplate in a large collection of hymnals.
The Cyber Hymnal includes two additional verses that are rarely sung but give even more of a feel for the ancient Celtic culture out of which which it arose.This Irish Culture and Customs site has a non-metrical translation of the poem.