Since it's St. Patrick's Day, I'm starting one. I don't drink and I hate crowds, so for me St. Paddy's is an excuse to play Irish music at top volume, and to sing in public without people asking me to stop. (The way I sing people assume I'm drunk, and you don't mess with drunks on St. Patrick's Day.)
My two favorite Irish songs are:
"Black Velvet Band"
& "Star of the County Down"
I recall one Eid al-Adha in Istanbul, with another American, an Australian, and a several Turks. The other American and Australian were drunk, the Turks were Turks, and the Asian part of Istanbul was mostly empty because of the holiday. So the Aussie started us off with a song as we danced down the streets arm-in-arm like people in an old movie, and I got to sing this song.
Here's one for Australia:
"Wild Colonial Boy"
Here's one which caused bad flashbacks for an English coworker. Apparently, while he was camping in Ireland, some drunken Irishmen surrounded his tent and sang Irish rebel songs all night long, and this was one of the songs they sang. If it does qualify as an Irish rebel song though, it's pretty mild as they go.
"Hills of Connemara"
Edit: Changed the title, since it's apparently distracted everybody from the point of the thread.