I hate to spoil yere grand session but you won't hear much singing in Irish pubs at all - TV or piped rock/pop is the standard background. Maybe some group that's well on might start slurring some song five minutes before closing time, but even then it's more likely to be some old pop chart topper from the distant past.
Visitors to Ireland often get a false sense of our pub culture because they visit tourist pubs where the famous one man ballad band is put on show to sing the same ould flahed-out reportoire that's been sung for the last forty years, i.e. anything ever recorded by the Clancys or Dubliners, with a few numbers from Christy to bring things up to date. Then of course you'll have to add a few rousing rebel songs so that the tourists leave, thinking we all hate the English.
Right, I know I'm being negative and that you can find pubs all over the country where they occasionally have sessions where you'll here a wide variety of Iris traditional songs sang in different styles. But unless you're in the know there're difficult to find.
I like almost everything that the Clancys and the Dubliners recorded but I don't want to live in a musical time warp from the 60's. I've been through it once and that's enouigh for me.
Apologies if my cranky rant upsets the thread.
Here's a nice song when sung in a pub or anywhere else:
"One Starry Night" http://www.youtube.com/watch?v=nEoCPFvRxtw