Gemara

(Beraisa - R. Meir): Something alive cannot be used for a Sukah wall, a Lechi, or Pasei Bira'os.

Sukah 23a (Beraisa - R. Meir): Something alive cannot be used for a Sukah wall;

R. Yehudah is Machshir.

Question: What is R. Meir's reason?

Answer #1 (Abaye): We are concerned lest it die.

Answer #2 (R. Zeira): We are concerned lest it go away.

All permit using a tied elephant. Even if it dies, the carcass will be a Kosher wall.

Berachos 5b (Beraisa - Aba Binyamin): I always exerted myself that my Tefilah should be near my bed.

Suggestion: This literally means near (facing) his bed.

Rejection: Rav Yehudah taught that when one prays, nothing should separate him from the wall in front -- "va'Yasev Chizkiyahu Panav El ha'Kir va'Yispalel"!

27a: A case occurred in which R. Yirmeyah bar Aba prayed in back of Rav. Rav finished first. He did not interrupt R. Yirmeyah's Tefilah.

Question (Beraisa - R. Eliezer): One who prays in back of his Rebbi causes the Shechinah to depart from Yisrael.

Answer: R. Yirmeyah bar Aba was a Talmid Chaver of Rav (a peer of Rav's who had learned from him).

Sotah 38b: A short person in back of a tall person receives Birkas Kohanim. (The latter is not a Chatzitzah.)

The Aron is not a Chatzitzah to prevent those behind it from receiving the Berachah.

Question: Does a (different) Chatzitzah block the Berachah?

Answer: No. R. Yehoshua ben Levi taught that even an iron wall does not intervene between Yisrael and Hash-m.

Rishonim

Rashi (27a DH v'Lo): Rav did not step back until R. Yirmeyah finished, lest he interrupt between R. Yirmeyah and the wall.

Tosfos (5b DH She'Lo): Something fixed, such as an Aron or Teivah, is not a Chatzitzah. However, it seems that a bed is a Chatzitzah.

Rashba (1:96): The Teivah (the platform on which the Shali'ach Tzibur stands and the Sefer Torah is read in a Sefardi Beis ha'Keneses), even though it is tall and wide, is purely for the needs of the Beis ha'Keneses. It is not a Hefsek (to be concerned that the Shali'ach Tzibur is not in the same Reshus as the Tzibur). It is like the Aron Kodesh. Even though it is tall, it is surely not a Hefsek, like it says in Sotah. This is because it is needed for the Beis ha'Keneses.

Poskim

Shulchan Aruch (OC 90:21): Nothing may interrupt between him and the wall. Something fixed, such as an Aron or Teivah, is not a Chatzitzah.

Rejection (Taz): What is Tosfos' distinction between a bed, and an Aron or Teivah? They move also the Teivah of the Beis ha'Keneses at times! During fasts for rain, they take it out to the street. Rather, these matters are needs of Tefilah in the Beis ha'Keneses, therefore they are not Chatzitzos. Therefore, the custom is in all Batei Kenesiyos that everyone has a Stender in front of him on which he puts his Sidur. It is not considered a Chatzitzah, even though it is 10 tall and four wide. This does not apply to a bed and other Kelim. Therefore, it is not considered fixed regarding Tefilah, and it is a Chatzitzah. I derive that a table in a house is not a Chatzitzah for Tefilah. It is needed for Tefilah, since one puts his Sefer on it. Even if something is a Chatzitzah between him and the wall, if it is not easy to pray without a Chatzitzah, e.g. when they pray in a room and not everyone can stand without a Chatzitzah between him and the wall, they should not delay due to this to go to another room. We avoid Chatzitzos lest they impair Kavanah. It is merely for the ideal Mitzvah. There is no Isur when there is a need due to limited space. In any case, if one closes his eyes at the time of Tefilah, or prays from a Sidur and does not look outside, the Chatzitzah will not distract him.

Magen Avraham (36): Why do people pray in front of a Stender 10 tall and four wide on which they rest a Sidur? Do not say that it is a need of Tefilah (and therefore permitted). The table and Teivah are also needed for Tefilah, yet they are permitted only if they are not fixed! Do not say that it is because they are not four wide at the bottom. Also a Stam bed is not four wide at the bottom! It is difficult to say that we discuss a bed that is solid until the ground. The Rashba connotes that it is because it is needed for the Beis ha'Keneses.

Machatzis ha'Shekel (DH uvi'Teshuvas): The Shulchan Aruch and Tosfos said that an Aron or Teivah is permitted because it is fixed. Perhaps they agree that needs of the Beis ha'Keneses are permitted. They gave one of two reasons why they are permitted.

Mishbetzos Zahav (5): The Magen Avraham rejected the Taz' answer that what is needed for Tefilah is permitted. I answer that what is outside four Amos is permitted, for it is a different Reshus. This explains how R. Yirmeyah prayed in back of Rav (according to the opinion that forbids in back of people - Sa'if 22). He was slightly more than four Amos in back, but Rav could not step back, for then he would enter R. Yirmeyah's four Amos.

Gra (DH u'Davar): The Gemara often discusses a Shali'ach Tzibur who goes "in front of the Teivah."

Kaf ha'Chayim (132): We do not distinguish a house from a Beis ha'Keneses. It depends only on whether or not it is fixed. However, some permit a table or Stender on which one rests his Sidur.

Mishnah Berurah (66): The Acharonim hold like the Taz, that needs of Tefilah are not a Chatzitzah.

Shulchan Aruch (ibid.): Animals are not a Chatzitzah. Even man is not a Chatzitzah.

Beis Yosef (DH u'Mah she'Chasav Rabeinu): The Tur says that animals are not a Chatzitzah. He did not specify whether this includes man. The Mordechai wrote that they (people) are not a Chatzitzah. This was obvious in Sotah regarding Birkas Kohanim. Mahari Avuhav learned from Berachos 27b, in which we say that one should not pray in back of his Rebbi. This implies that one may pray in back of other people. This is a good proof.

Bedek ha'Bayis: The Yerushalmi explicitly says so.

Rema: I say that animals are a Chatzitzah, but man is not. It seems that the Poskim hold like this. Perhaps there is a printing mistake (in the Mechaber).

Pri Chodosh (21): Presumably, animals are not a Chatzitzah, like the Mechaber says. We find that animals can be a Sukah wall (Eruvin 15b, Sukah 23a). Here also, it is like a Mechitzah, and it is not a Chatzitzah. One may pray in back of a person, except for a Talmid in back of his Rebbi. This shows that a person is not a Chatzitzah. Surely, an animal is no different. One who is stringent not to pray in back of a person is called a Hedyot (commoner), for he does what he is exempt from, unlike the Mechaber (in Sa'if 22).

Rebuttal (Sha'arei Teshuvah 29): He is not called a Hedyot, for he is passive. He does not refrain from praying with the Tzibur due to this. The Mechaber agrees to this!

Gra (DH Adam): We learn from Berachos 27b that man is not a Chatzitzah. The Mechaber holds that all the more so, animals are not a Chatzitzah. The Rema disagrees.

Kaf ha'Chayim (134): Also the Bach and Levush say that there is a printing mistake in the Mechaber. Therefore, we hold that animals are a Chatzitzah. Yafeh l'Lev says that also, an animal has no intelligence. Perhaps it will urinate or defecate while the person prays facing it.

Shulchan Aruch (22): Some say that one should not pray in back of a person. It is good to be concerned for this opinion.

Beis Yosef: (Even though Mahari Avuhav brought a good proof from Berachos 27b,) Sefer ha'Pli'ah says that one must be careful not to pray in back of any person. It is good to be concerned for his words.

Mishnah Berurah (69): Ma'amar Mordechai says that it is impossible to be careful about this. How can everyone stand opposite the wall without anyone in between?! Even though this opinion holds that it is not a real Hefsek. It is mere carefulness when it is possible. Surely it is permitted l'Chatchilah in a Beis ha'Keneses, just one who is meticulous will fix his place opposite the wall.

Kaf ha'Chayim (135): Erech Lechem and Lechem Yehudah say that a person engaged in Tefilah is not a Hefsek. Ma'amar Mordechai says that the Mechaber connotes unlike this.