OK, here are my recs for traditional, ballad-esque songs. Most of these you can get off iTunes in some form or another. I have my favored versions, but you can sort of shop around for your own
"Lagan Love" (sometimes preceeded by "My"): Possibly the epitome of haunting Celtic tunes, at least in my opinion. It's one of those that's great with accompaniment, but even better as a solo voice, because the melody is so rich and evocative. There's a lovely guitar and voice version from Al Petteway and Amy White. William Coulter also has a nice solo guitar version.
"Wild Mountain Thyme": Sometimes up tempo, but best when down tempo. My favorite version is by Kathleen Keane. You can't find it on iTunes, but ifyou want to splurge and get her album (only online, as far as I know), she's a really incredible musician: fiddler, vocalist, most insanely fabulous whistle player I've ever heard.
"Sea Image": from the Chieftains. Gorgeous.
"The Wounded Hussar": Another great solo. My favorite is from Lunasa, one of my favorite Irish groups. Very original sound.
"Black is the Color": A classic. TONS of choices here, but for this one, I have to go with my favorite band on the face of the planet, Gaelic Storm.
Actually, lucky for you, they've got a lot of their music online at their website:
http://gaelicstorm.com/?inc=albums&sm_ord=3482 "Black is the Color" isn't available for listening, but you should check out "An Cailin Deas Rua" for a really beautiful song sung in Gaelic

Heck, listen to all of it! I've not met many people, regardless of musical taste, that didn't like Gaelic Storm
