There are different layers of Halachic issues regarding the reading of newspapers on Shabbat. One issue is the content of the paper. That is, certain content is prohibited to be read on Shabbat because it is considered mundane and inappropriate for Shabbat reading. In fact, many of today’s newspapers and magazines are not even suitable for weekday reading.
Nevertheless, even if the content of the newspaper is permissible, there is still a question as to whether it may be read on Shabbat, because it was delivered by a non-Jew on Shabbat. The Halacha is prohibits subscribing to a newspaper delivered on Shabbat, because it is tantamount to directing the non-Jewish delivery agent to perform the melacha of carrying on Shabbat.
If a person, nevertheless, violated this prohibition, and a newspaper was delivered on Shabbat, it is forbidden to read the newspaper on Shabbat. In fact, the newspaper is muksa and cannot even be moved or brought into the house. The reason is that one is not allowed to benefit from melacha that was done for a Jew on Shabbat until after Shabbat. According to the Be’er Moshe (Ch. 95), it is permitted on Mosei Shabbat only "Bichdai Sheya'asu." That means the time that it would have taken that newspaper to be delivered on Mosei Shabbat. If it takes the delivery boy half an hour to bring the paper from the place he picks them up, then one would have to wait a half hour after Habdalah before reading the newspaper. The Shemirat Shabbat K’hilchata is a little more lenient. He ruled that one doesn’t have to wait "Bichdai Sheya'asu;" it can be read right away on Mosei Shabbat. This applies to cases in which the newspaper was delivered in violation of the Shabbat. However, if the subscriber stipulated that he is not interested in Shabbat delivery, and nevertheless, the paper was delivered, it is permissible to read on Shabbat.
There is no problem having mail delivered on Shabbat, since the Jew did not request that it arrive specifically on Shabbat. Therefore, it is permitted to read "kosher" magazines that happen to arrive on Shabbat.
SUMMARY
One should cancel his subscriptions to newspapers that arrive on Shabbat. If one cannot cancel the subscription totally, he should at least stipulate to the company that he is not interested in Shabbat delivery.
Newspapers delivered on Shabbat, in violation of the Halacha, are muksa and cannot be read until after Mosei Shabbat.
