The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes (Parashat Vayeseh) that the modern practice of cleaning oneself after defecating with dry paper, without using water, is Halachically incorrect. Halacha forbids praying, reciting Berachot or earning if even a tiny amount of excrement is present on the body, and it is impossible to ensure the complete elimination of all traces of excrement from the surface of one's body without water.
It is therefore strongly advisable when possible to have a bidet installed in one's restroom so he can clean himself with water. If one does not have a bidet, or uses a restroom that does not have a bidet, he must at least use moist toilet paper, or moisten the toilet paper before cleaning himself, so he ensures to clean himself properly. If one has no possibility of cleaning himself with water, then he must take the time to clean himself very well with paper.
The Shulhan Aruch (Orah Haim 3:11), based on the Gemara (Shabbat 82a), writes that one should not use a flammable material to clean himself after defecating, as this could pose danger. The Rama (Rav Moshe Isserles, Poland, 1530-1572) cites the Sefer Ha'aguda (Rav Alexander Suslin, Germany, d. 1349) as claiming that this applies only when one is outside a city, where there is a risk of evil spirits. Under normal circumstances, however, there is no concern when cleaning oneself with a flammable material. The Rama writes that he does not understand the rationale of this distinction, but he acknowledges that common practice is to disregard this warning and allow using flammable material for cleaning oneself. The Magen Abraham (Rav Avraham Gombiner, Poland, d. 1682) suggests that in open areas, outside the city, one is exposed to spells cast by magicians, and this is the reason for the distinction drawn by the Sefer Ha'aguda. In any event, the Aruch Ha'shulhan (Rav Yechiel Michel Epstein, 1829-1908) writes that as these magicians are no longer common in the modern world, we need not be concerned, and thus people do not hesitate to use flammable paper to clean themselves.