Klingon drinking songs are songs that Klingons sing about drinking bloodwine, having glorious battles, the Empire, among other things. So, pretty much every Klingon song you hear, with the exception of a few, could actually be considered Klingon drinking songs.
On the Starship Voyager, The Doctor wanted to get Seven of Nine to learn a Klingon drinking song. Her response was "I fail to see the merit of learning a Klingon drinking song," to which the doctor replied: "It’s not about drinking, Seven, it’s about saluting the noble deeds of our ancestors. And honoring those who fell in battle. Think q’pla! Think long live the Empire!" (VOY: "Barge Of The Dead")
The Doctor once mentioned that B'Elanna Torres's appreciation of music is limited to a smattering of Klingon drinking songs. (VOY: "Virtuoso")