I'm using firefox.
I've just discovered something. The ads are only there in one skin.
The ads only appear in the skin tff blue. I use that when I'm logged in and "IP board classic blue (import)" when I'm not logged in - different ones so I can tell at a glance whether I'm logged in or not. When I logged out earlier and the ads vanished, I assumed it was a logged in/out thing. But then it occurred to me about the different skins, so I checked them all out, and of the whole list it's only tff blue that shows the ads.
If the ads annoy you, change skins!