Gemara

(R. Elazar): Anyone who does not leave bread on the table will never see a Siman of Brachah - "Ein Sarid l'Achlo..."

Question: R. Elazar taught that leaving pieces on the table is like serving idolatry - "ha'Orchim la'Gad Shulchan"!

Answer: It depends on whether there is a full loaf with the pieces.

Rishonim

Rosh (11:3): Anyone who does not leave bread on the table will never see Brachah - "Ein Sarid l'Achlo..."

Rashi (92a DH Kol): One must leave pieces on the table due to "eat, and there will remain." If there are pieces and he brings a full loaf, it looks like he does so for idolatry. If there is not a full loaf with the pieces, it is proper, for they (the pieces) are for poor people.

Poskim

Shulchan Aruch (OC 180:2): Anyone who does not leave bread on the table will never see a Siman of Brachah.

Magen Avraham (1): Berachah does not rest on something empty, rather, only when there is something, like Elisha and the Shunamis. (She had only a little oil, and miraculously it filled all the Kelim she could borrow.)

Machatzis ha'Shekel (1): Had she not had any oil to begin with, Hash-m would not have created oil for her. Hash-m created everything from nothing in the six days. After, it is His desire to create only from what already exists.

Mishnah Berurah (2): One must leave pieces in case an Oni will come, and also to thank Hash-m for His Chesed, that we were satiated and there was left over.

Kaf ha'Chayim (4): The Zohar is very stringent about blessing on an empty table. It makes an Asmachta and calls this "taking Hash-m's name b'Shav (in vain)."

Kaf ha'Chayim (5): Meticulous people do not leave an empty Keli on the table. One should not leave a spoiled or repulsive food on the table, for "this is the table that is in front of Hash-m."

Shulchan Aruch (ibid): One should not bring a full loaf. If he did, it looks like it is for idolatry - "ha'Orchim la'Gad Shulchan."

Beis Yosef (DH Garsinan): If there are no pieces on the table and he brings a whole loaf, it looks like he brings so it will be ready for an Oni.

Drishah (DH Agav): A full loaf fulfills "eat, and there will remain", but it does not fulfill leaving for an Oni, for it is not destined to be given to an Oni.

Magen Avraham (2): The Shulchan Aruch connotes that if there is already a full loaf he need not remove it, and so says Be'er Sheva and a Hagahah in Beis Yosef in the name of the Zohar in Terumah, and so one may infer from Rashi. Asis Rimonim says that one leaves pieces if he cannot leave a full loaf for Birkas ha'Mazon; this is better, based on the Zohar in Yisro. The Gemara connotes that when there is a full loaf with the pieces, he must remove it. Mahariyo says so. Mateh Moshe says that one should be concerned for this, but he did not see the Zohar. Perhaps the Zohar explains the Gemara. If he has a full loaf on the table and he brings pieces, it looks like he does so for idolatry. This fits the Gemara better than Rashi's Perush. The Zohar agrees that one may not bring a full loaf at the time of Birkas ha'Mazon. On Shabbos one should not remove the full loaf until after Birkas ha'Mazon.

Shach (YD 178:5): Perhaps Mahariyo says to remove the bread only when they brought a full loaf after they ate. His words do not connote like this, but it is best to resolve his words if possible.

Kaf ha'Chayim (6): Mahariyo says to remove it because Berachah does not rest on something counted, and a full loaf is like something counted. However, this is unlike many Poskim and the Zohar in Yisro. When something is not explicit in the Gemara, and Poskim argue about it, we follow the Zohar.

Mishnah Berurah (4): If there are no pieces on the table, one may bring a full loaf. The Zohar says that it is good to do so l'Chatchilah.

Kaf ha'Chayim (7): If there are no pieces on the table, he should not bring a full loaf. If he brought a full loaf, he should eat a little, so it will not be full, and it will seem that he brought it to eat. This is like the Zohar and the simpe reading of the Shulchan Aruch.

Mishnah Berurah (5): The Magen Avraham says that if there is a ful loaf, one may not bring pieces. The Pri Megadim says that similarly, if there is a full loaf, one may not leave pieces. Some allow leaving them. On Shabbos surely one may leave the pieces and loaf, for all know that they are left for Kavod Shabbos.

Shulchan Aruch (YD 178:3): One who ate and left pieces on the table may not bring a full loaf and leave it on the table.

Beis Yosef (DH Garsinan): This is like Rashi explained. I do not know why the Poskim omitted this.

Shirei Keneses ha'Gedolah (Hagahos Beis Yosef 8, cited in Hagahos Tur ha'Shalem 17): Be'er Sheva says that perhaps it is because we hold that the idolatry Gad is not found nowadays.

Kaf ha'Chayim (OC 180:8): The Ari Zal would leave drops of wine in the cup of Kidush or Birkas ha'Mazon, so that Berachah would remain on Shabbos night. He would leave pieces and crumbs under the cloth, but not a full loaf, due to ha'Orchim l'Gad Shulchan. This is like the Levush. We follow this.

Rema: In some places they set a table full of food on the night before a Bris. This is forbidden due to ha'Orchim l'Gad Shulchan. Some permit to set a bed for the Mazal of the baby.

Shach (6): There is no Isur to have a Seudah the night before. It is Asur only to set the table (not to eat now) and leave the food on it.

Pischei Teshuvah (2): This connotes that there is no Mitzvah to make a Seudah the night before. Also Chavos Ya'ir 70 says so.

Dagul me'Rvavah: Tosfos (Bava Kama 80a DH l'Bei) explains that there was a custom to make a Seudah when a boy was born out of gratitude that he survived birth. The Terumas ha'Deshen says that it was made on Shabbos night, when people are home. If so, they should do so also for girls! Rather, it was intended to be close to the Mitzvah of Milah.

Levush: The primary reason to leave bread on the table is so it will be ready for an Oni who may come. This is why they said to leave only pieces. Bringing a full loaf looks like idolatry. Therefore, one should protest against those who set a table full of food on the night before a Bris. Likewise, one should protest against those who set the table on Shabbos night with a full loaf and leave it the entire night. I heard some say that this is a commemoration of the Man that was in a box (covered above and below with dew) the entire night, therefore, we cover the bread with a cloth the entire night. This is wrong. The Man fell in the morning - "uva'Voker Haysah Shichvas ha'Tal"! Surely this custom originated from an idolatrous rite, so one should protest.

Rebuttal (Taz 7): Only regarding a Bris, which is done for the Mazal of the baby, this pertains to ha'Orchim l'Gad Shulchan. 'Gad' is an expression of Mazal (see Rashi Bereishis 30:11 - PF). Leaving two loaves on the table on Shabbos night is to honor Shabbos, which is honored through two loaves. It does not depend on Mazal at all. It is not forbidden at all. Also on Erev Shabbos, once we remove the bread from the oven we put it on the table for Kavod Shabbos!