Funnily enough, a drinking song is a song sung whilst drinking alcohol- and they are usually folk songs. In some places, they even have specific names, such as Trinklieder (Germany).
According to my sources, there isn't much else to say about this genre... So let's get on with the examples! Just a small note- the lyrics to these songs are also often rude and crude. What a surprise.Listen at your own discretion. Alternately, if you're immature (possibly like moi) you can have a little chuckle.
I Used To Work In Chicago- Eddie Vedder
Fathom The Bowl- Rogues Gallery