Discussion: "Ritual objects" is a general term which, in halachah, breaks down into a number of different categories. How one should "dispose" of a given ritual object is determined by the category into which the object falls. In the initial breakdown, ritual objects are classified as either kedushah objects, which may not be discarded at all, and used mitzvah objects, which may be.
Kedushah objects are intrinsically holy (such as a Sefer Torah). The category below them, tashmishei kedushah, are objects which serve or beautify the kedushah objects (such as a Torah mantle, which beautifies the Torah scroll). An even lower category is tashmish d’tashmishei kedushah, which are objects that serve or protect the tashmishei kedushah, not the kedushah object itself (such as a plastic tefillin bag, which protects the velvet tefillin bag).
Used Mitzvah objects are objects with which one performed a mitzvah (such as an esrog). The category below them is objects which serve as accessories for performing the mitzvah (such as an esrog box). These are referred to as tashmish d’tashmishei mitzvah.
Question: How may one "dispose" of kedushah and tashmishei kedushah items?
Discussion: It is strictly forbidden to destroy or dispose of items that are intrinsically holy, even when they are no longer fit to be used. Moreover, even tashmishei kedushah, which are objects that serve or beautify the kedushah object itself, may also not be destroyed or thrown away even when their condition has deteriorated. Rather, they must be set aside and stored in a safe, secluded, permanent and honorable place – a process called genizah. Since it is not so feasible or practical to find such storage places, especially for larger collections of objects, the halachah permits burying kedushah and tashmishei kedushah in the ground – genizah b’karka. There are two levels of genizah b’karka, depending on the degree of their kedushah:
Strict genizah: Some objects require strict genizah. These items must be encased and sealed in an earthenware or durable hard plastic casing and buried in a Jewish cemetery, preferably together with or in the vicinity of a grave of a Torah scholar or in a specially designated section of the cemetery.
Standard genizah: The objects on this list may be bagged in a nylon or plastic bag and buried anywhere (not necessarily in a cemetery), as long as it is a secure place where the objects will not be disturbed. Nowadays, this type of genizah is generally referred to as sheimos genizah.
Question: Which objects require strict genizah and for which will the standard genizah suffice?
Discussion: The following items require Strict genizah:
- An amulet that contains Hashem’s Name
- Mezuzah parchment
- Nevi’im, Kesuvim and Megillah scrolls 
- Sefer Torah scroll
- Tefillin, bayis shel rosh (even without parashiyos)
- Tefillin, parshiyos 
The following items require Standard genizah (sheimos):
- An amulet holder (case)
- Aron kodesh
- Bentschers and zemiros booklets 
- Bimah cover – embroidered
- Hashem’s Name (handwritten or printed)
- Mezuzah case, including any plastic or saran wrapper
- Sefer Torah accessories – atzei chayim, band, bell, crown, mantle, pointer and silver ornaments
- Sifrei kodesh – printed or photocopied, hard or soft cover
- Sifrei Kodesh – covers, binding, and bound, blank pages
- Tefillin, bayis shel yad (without parashiyos)
- Tefillin, plastic protective boxes 
- Tefillin bag, velvet
- Torah manuscripts
Question: What are the rules for disposing of used mitzvah objects?
Discussion: Used mitzvah objects include "intrinsic" mitzvah objects, such as a shofar or a lulav, which were previously used in the performance of a mitzvah but are no longer needed – either because the objects are in poor condition or because the mitzvah is no longer applicable. Although a minority opinion holds that these items should receive standard genizah and the Rama praises one who does so, the basic halachah and the prevalent custom follow the opinion that it is permitted to discard these items in a dignified manner. It is forbidden, therefore, to throw these items directly into the garbage. Rather, they should first be wrapped up or placed in a bag, and then put in the recycle bin or together with "clean" trash. Alternatively, they may be burned.
The following items may be discarded, but only in a dignified manner:
- Arba’as ha-Minim 
- Oil and used wicks remaining from Chanukah menorah
- A Shofar
- Tzitzis strings (detached from a tallis)
- A tallis gadol (with tzitzis)
- A tallis katan (with tzitzis)
Question: What are the rules for disposing of tashmish d’tashmishei kedushah and tashmish d’tashmishei mitzvah objects?
Discussion: This lowest category of ritual objects includes those items which are not directly involved in either the kedushah itself or in the direct performance of a mitzvah. The basic halachah holds that once these items are no longer fit for use, or once the mitzvah that they were used for is no longer applicable, they have no significance whatsoever and require no special method of disposal. It is still recommended by many poskim, however, that in order to show honor and respect to a mitzvah, it is appropriate to dispose of these items in a dignified manner only.
The following items may be discarded in any manner, but it is recommended that they be disposed of with respect:
- A Kiddush cup ("becher") – used for Kiddush and Havdalah only
- A bimah 
- A bimah cover, plastic
- A bookcase (used exclusively for sifrei kodesh)
- Candlesticks (used for Shabbos candles) and leftover wicks 
- A Chanukah menorah
- An esrog box
- A Havdalah candle
- Havdalah spices
- A Lulav case and rings
- The nails used to affix a mezuzah case to the doorpost
- The paroches of an aron kodesh
- Succah walls and decorations 
- A Tallis gadol (without tzitzis)
- A Tallis katan (without tzitzis)
- A Tallis bag, velvet
- A Tefillin bag, plastic
2.See Rambam, Sefer ha-Mitzvos, Lo Sa’aseh 65; Kiryas Sefer, Hilchos Sefer Torah 10 and Chasam Sofer, O.C. 38.
3.Magen Avraham 154:9.
4.O.C. 154:5, as explained by Noda b’Yehudah, Tanina, O.C. 9; Binyan Tziyon 97; Aruch ha-Shulchan 154:8; Minchas Elazar 3:52; Igros Moshe, O.C. 4:38; Tzitz Eliezer 15:8.
6.Marcheshes 1:53; Gesher ha-Chayim 33:3. This is the custom today; see Ginzei ha-Kodesh 15:7.
7.Peri Megadim, Eishel 154:9 (quoted by Mishnah Berurah 154:22). See also Mishnah Berurah 154:13, as explained by Tzedakah u’Mishpat 15, note 65.
8.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 6:26).
9.Rav Y.S. Elyashiv and Rav N. Karelitz (Ginzei ha-Kodesh 15:1).
10.Mishnah Berurah 154:22.
12.Rav Y.S. Elyashiv and Rav N. Karelitz (Ginzei ha-Kodesh 6:6). Other poskim require standard genizah only.
13.Rav Y.S. Elyashiv and Rav N. Karelitz (Ginzei ha-Kodesh 15:1); Kinyan Torah 3:47.
14.Mishnah Berurah 154:14.
16.See Igros Moshe, Y.D. 2:135 and Ginzei ha-Kodesh 10:17.
17.Mishnah Berurah 154:10-11 — even if it is always protected by a plastic cover; see Piskei Teshuvos 154, note 49.
18.See Y.D. 276:9-10 for the seven Names of Hashem which require genizah.
20.Based on Mishnah Berurah 154:14 and Beiur Halachah, s.v. v’davka. See also Mezuzos Beisecha 291:5 and Ginzei ha-Kodesh 6:21-22.
22.Aruch ha-Shulchan 154:5.
23.Mishnah Berurah 40:4, 154:7; Chazon Ish, Y.D. 164:3.
24.Mishnah Berurah 40:4, 154:9; Rav Y.S. Elyashiv, quoted in Ginzei ha-Kodesh 8:10.
25.Rav Y.S. Elyashiv and Rav N. Karelitz (Ginzei ha-Kodesh 6:6).
26.Mishnah Berurah 154:7 and Sha’ar ha-Tziyun 7.
27.Minchas Elazar 1:27. In addition, anything made especially to honor an item of kedushah, such as an embroidered tefillin bag, is considered tashmishei kedushah even if it does not touch the kedushah itself; see Beiur ha-Gra, Y.D. 282:33 and Mishnah Berurah 154:9 and 14.
28.O.C. 21:1. Indeed, many people are careful to burn their lulav (together with the chametz) for this reason.
29.Mishnah Berurah 21:6.
30.Sha’ar ha-Tziyun 664:20.
31.O.C. 677:4. It is customary to burn them and not discard them even in a respectful manner.
33.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 17:13).
35.See Kaf ha-Chayim 297:11 and Ginzei ha-Kodesh 20:5.
36.Kaf ha-Chayim 154:12; Tzedakah u’Mishpat 15, note 45. [Although Mishnah Berurah 154:10 and Sha’ar ha-Tziyun seems to hold that a bimah requires standard genizah, he contradicts himself in 141:4.]
37.Mishnah Berurah 154:9 and most poskim. But some poskim consider a bookcase as tashmishei kedushah, and require genizah. In order to avoid the issue, it is recommended to “redeem” the bookcase, a process detailed in Mishnah Berurah 153:62; see Imrei Yosher 1:45; Chelkas Yaakov 3:162; Tzitz Eliezer 7:7.
38.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 19:12).
39.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 19:13).
40.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 18:20).
41.Chovas ha-Dor 1, note 43.
42.Mishnah Berurah 154:11.
43.Mishnah Berurah 21:6.
44.Rav C. Kanievsky (Ginzei ha-kodesh, pg. 270).
45.Rav Y.S. Elyashiv (Ginzei ha-Kodesh 17:13).