The Shulhan Aruch (307:13-14) prohibits reading any documents connected with business or finances. For example, one may not review a telephone bill, receipt or letter of credit on Shabbat, whether he reads it aloud or silently. The Poskim offer several reasons for this prohibition. Some say that it is derived from the Pasuk of, "Mimso Hefseha"-conducting business. The Rambam learns that one may come to erase words from the document.
Moreover, Maran prohibits reading "Igrot Shalom"-interpersonal correspondence, even if not connected to money. Maran permits only to read a letter that arrived on Shabbat which may contain urgent information needed immediately. Even then, he only allows reading it with the eyes, and not verbally.
Rav Moshe Feinstein (Russia New York, 1895-1986) in his Iggerot Moshe (OC 5:25) discusses whether this leniency applies today when it is very rare for critical information to be delivered by regular mail. Most urgent messages are communicated by telephone or Email. He concludes that we cannot suspect that a letter contains such urgent information, and there is no room to permit reading it, even if it was delivered from within the Tehum (boundary) Shabbat.
The Mishne Halachot (Rav Menashe Klein, 1924-2011, Brooklyn, in Vol. 6:70) agrees in theory with Rav Moshe, but is reluctant to prohibit it, since the Mishna Berura is lenient, and there are precedents of great Hachamim who relied on this leniency, even though there were telegrams in their day. The Shemirat Shabbat K'hilhata (Ch. 29, note 117) cites Rav Shlomo Zalman Aeurbach who also seems to be lenient. Those who have a clear and pressing concern that a letter may contain vital information, may rely on the lenient opinions. Of course, they may only read it once, with their eyes.
These Halachot illustrate how a person may think that they are Shomer (observe) Shabbat, but in fact they violate these prohibitions, which seem so innocuous. Unfortunately, people tend to read catalogs and the like, which is a clear violation of Shabbat. One of the other reasons given for these prohibitions is that Shabbat was given to study Torah, and not to read mundane material. This is the opinion of Rambam in his commentary on the Mishna (Shabbat Ch. 23), the Hayeh Adam and the Seda Laderech. Needless to say, these prohibitions apply to reading material that is permissible to read during the week. Otherwise, it should be avoided all week long.
It is prohibited to read bills and other business related documents on Shabbat, even if read with the eyes alone. It is also not permitted to read any mundane correspondence, unless there is a clear and pressing concern that it may contain critically urgent information needed on Shabbat.