No the 2nd generation ipod Touch cannot be jailbroken. Don't even try it til they say it can on Dev-Team Blog (They are the makers of QuickPwn and PwnageTool, any other site claiming such is lying.)
and yes I know there's some fake youtube videos claiming it can be.
Course if thats what they said, then you know it's fake, because the 2nd gen never shipped with anything lower than 2.1.1 (also it seems some folks don't know what a 2nd gen is, they just think it's a ipod with firmware 2.0+ on it, as such a false positive).
Simply put, until the iPhone dev team gets back to it (which they won't til they finalized the unlocking of the iphone 3G), the 2nd gen cannot be jailbroken, nor has had ever had a firmware capable of jailbreaking.
There was ZiPhone for the older iPhones and iPod Touches that still had firmware 1.1.4 and below on them, then QuickPwn/PwnageTool is for the iPod Touch(1st gen only), iPhone and iPhone 3G with firmware 2.* on them.
Attempting to use QuickPwn or another on the 2nd gen can usually be recovered by restoring it with iTunes... however trying to use ZiPhone (which is definitely not intended for a 2.* firmware device), could potentially brick it.