Siddur

In Sha'ar HaKavanot, Rabbi Chaim Vital (a disciple of the Ari) explains why various liturgies are used among different segments of the Jewish world:

There are many differences between the [various] prayer books, between the Sefardic rite, the Catalonian rite, the Ashkenazi rite, and the like. Concerning this matter, my master [the Ari] of blessed memory told me that there are twelve windows in heaven corresponding to the Twelve Tribes, and that the prayer of each tribe ascends through its own special gate. This is the secret of the twelve gates mentioned at the end of [the book of] Yechezkel. There is no question that were the prayers of all the tribes the same, there would be no need for twelve windows and gates, each gate having a path of its own. Rather, without a doubt it necessarily follows that because their prayers are different, each and every tribe requires its own gate. For in accordance with the source and root of the souls of that tribe, so must be its prayer rite. It is therefore fitting that each and every individual should maintain the customary liturgical rite of his forefathers. For you do not know who is from this tribe and who from that tribe. And since his forefathers practiced a certain custom, perhaps he is from that tribe for whom this custom is appropriate, and if he comes now and changes it, his prayer may not ascend [to heaven], when it is not offered in accordance with that rite.

— Sha'ar HaKavanot, Inyan Nusach HaTefila

Nusach Ashkenaz - The prayer rites followed by non-Chassidic Ashkenazi Jews of Western and Central Europe and beyond.

Nusach Sefard - The siddur followed primarily by Chassidic Jews, and based on the teachings of the Arizal.

Nusach Eidot Hamizrach - Sephardic Jews follow several slightly different but closely related rites, rather than a codified nusach. Today's Nusach Eidot HaMizrach originated among Iraqi Jews, but today is in wide use among Sephardim of many backgrounds. The text relies heavily on the teachings of the Ben Ish Chai (Rabbi Yosef Hayyim of Baghdad) and has extensive Kabbalistic influences.

Spanish & Portuguese Jews - A variant of the Sephardic rites based on an older form of the Castilian rite, with some influence from the customs both of Italian Jews and of Northern Morocco. This version is distinguished by the near-absence of Kabbalistic elements.

Minhag Aram Soba, as used by Syrian Musta'arabi Jews in earlier centuries. Today's Syrian rite is closely based on the Livorno prints.

Moroccan - Related to the text found in the Livorno siddur prints but with a strong local flavor. 

Nosach Teiman - The Yemenite prayer rite is divided into the Baladi (purely Yemenite) and Shami (adapted from Sephardic siddurim) versions. The Baladi rite is similar to that codified by the Rambam in the Mishneh Torah. Both rites are recited using the unique Yemenite pronunciation of Hebrew, which Yemenite Jews, and some scholars, regard as the most authentic, and most closely related to the Hebrew of Ancient Israel. 

Nusach HaGra - A version of Nusach Ashkenaz based on the teachings of the Vilna Gaon, leaving out certain passages which he held were not found in the original prayer text, an incorporating grammatical changes which he set forth to correct errors he felt had made their way into the text.

Minhag Benè Romì and Minhag Italiani - Used by some Italian Jews, as well as by a small number of congregations in Jerusalem and Netanya.

Romaniote - The surviving Romaniote synagogues are in Athens, Ioannina, Chalkis, Jerusalem, Tel Aviv and New York (and formerly in Istanbul). Today these congregations follow a Sephardic rite with Romaniote variations.