In Ketzos HaShulchan volume 4, R' Avraham Chaim Na'ah (Badai HaShulchan 107:43) brings the ruling of R' Yaakov Emden [Responsa 306 of She'elat Ya'avetz] that reading publications that have in them discussions of business is forbidden on Shabbat.
R' Avraham Chaim Na'ah explains that this refers to even intending to read just the news (which is technically permitted on shabbat, since it is necessary to know what's going on and brings one pleasure to read it - and pains one not to read it) and skipping over the business parts, since it is impossible to make sure you don't read the business parts at all.
[Although he doesn't discuss this explicitly, I think advertisements might fall under the category of business. If so, one couldn't read any publication that had advertisements, since it is impossible not to see them]
Based on this, R' Na'ah originally thought to permit reading publications made by Bnei Torah which don't have business in them at all, but are made to strengthen Torah observance. R' Na'ah concludes however, that one shouldn't even read those publications on Shabbat, since sometimes when one reads them he is pained by the plight of Orthodox Jewry around the world, and it is forbidden to discuss/read about matters that pain you on Shabbat.
R' Na'ah then says that all this is talking about publications that are made by Torah Observant people. Other publications include many things that are forbidden to read even during the week, such as heresy, frivolity, etc. And just like on Shabbat, one can't say he'll only read the "kosher" sections, since it is impossible to limit what you see that way. [makes me wonder what he'd say about the internet]