O'Donoghue's Bar, which dates back to the eighteenth century, is arguably the most famous pub in Dublin for traditional Irish music.
The bar is lively, rammed with a mainly—but by no means exclusively—local crowd, and has a great, welcoming atmosphere. There is a huge beer garden, and on busy nights there will be someone serving the tables outside.
The main draw, of course, is the live traditional music, which kicks off mid-evening seven days a week. Unlike many other venues that boast live trad and there is no sense that the music at O'Donoghue's is a performance put on for the tourists. In fact it's quite the opposite: you get the feeling the musicians are playing solely for themselves, and don't care whether you listen or not. Which is lucky, really—the night we were there the bar was so crowded, and the conversation so raucous, that you had to get really close to hear the music.
If you're a fan of, or curious about, traditional Irish music, O'Donoghue's is definitely a place to check out. And make sure to keep your eyes open as well as your ears: such local musical luminaries as the Dubliners and Christy Moore have been known to swing by in the past!