I just got an advertising offer from one of those Internet Ad providers. The question is, would you allow pop-under ads for your website?

Personally, I find them really annoying. My past experience with pop-under ads was when I added a shoutbox to my old blog, the code ran pop-under ads for any visitor using Internet Explorer. I ditched that shoutbox as soon as I realized what was going on (I use Firefox almost all the time).