Sometimes what I see happen is certain article pages that aren't linked to a menu item load all the module from the home page because there isn't another page for them to load on.
I was experiencing this issue mentioned above, and I did have success directly controlling through the menu assignment inside the module, just like Mike said.
So for example, all of my pages have modules in the "right" position, and I wanted to keep these modules on all pages
except on individual article pages. I have all of my articles in categories such as "community" and "education". Inside the modules which I wanted to remove from my articles, I changed the module assignment to include all pages except for those particular categories. I hope that helps!