The Levush (quoted in ערה"ש או"ח סי רפ"ה ס"ק א) used the opening words of this week's parsha, ואלה שמות בני ישראל as an acronym for the phrase וחייב אדם לקרות הפרשה שנים מקרא ואחד תרגום, that one must read each weekly parsha twice and its targum once, and this obligation applies to the entire בני ישראל. The earliest mention of this obligation of שנים מקרא ואחד תרגום is in the Gemara (ברכות ח), which states לעולם ישלים אדם פרשיותיו עם הציבור שנים מקרא ואחד תרגום ואפילו עטרות ודיבון, "One is required to finish his parshiyot with the community, reading the text twice and targum once, even for Atarot and Divon (a seemingly unimportant pasuk in a long list of cities)." The Gemara adds that the reward for one who does this is longevity. The obligation is unquestionably מדרבנן (see ערה"ש שם סע' ב), as the Gemara makes no attempt to find a Biblical source, but its rationale is not completely clear. Mateh Moshe (quoted by קונטרס אחרון to טעמי המנהגים ומקורי הדינים סי' שמו) suggests that the text is read twice to parallel the giving of the text at Har Sinai and in Ohel Moed (see Rashi to סוטה לז:, who explains that after the Mishkan was erected Hashem spoke to Moshe from the Ohel Moed and taught him the entire Torah), and the targum is read once to parallel the Torah that was written by Yehoshua באר היטב, which Chazal interpret as being written in seventy languages (see Rashi to דברים כז:). Levush suggests that it was instituted in order to ensure that all Jews would know the Torah well (וכ"כ בהקדמה לספר החינוך). However, this approach is generally rejected, because most ראשונים and אחרונים assume that if there were such a simple reason for the obligation, it would not contain so many complex details (see ערה"ש שם). Rather, most halachic authorities maintain that the obligation to do שנים מקרא ואחד תרגום was established as an obligation on each individual which parallels the communal קריאת התורה in its nature. This understanding fits in well with the requirement to do each parsha during the week that it is read in shul, and it also explains the Gemara's precise language of "finishing one's parshiyot with the community."
Raavan (תשובות ס' פ"ח; quoted in דברי חמודות לברכות שם אות מא) explains the requirement to read the text twice and the targum once as an imitation of communal Kriat HaTorah, where there are two people reading the text (the Baal Korei and either the gabbai who follows along and checks, or the person who receives the aliyah, עיי"ש ובמעדני יום טוב אות ד), and the מתורגמן translating into Aramaic (as was the practice in Talmudic times). He thus believes that the obligation to do שנים מקרא ואחד תרגום was only established for one who misses the Torah reading in shul to make up what he missed. He is required to do שנים מקרא ואחד תרגום in order that he will complete the entire Torah on Shemini Atzeret/Simchat Torah and not be missing the parshiyot from those weeks when he did not attend shul. Rambam (הל' תפילה יג:כה) and Shulchan Aruch (או"ח רפה:א) reject Raavan's opinion outright by stating, "Even though one hears the Torah every Shabbat in shul, he is required every week to read that week's parsha on his own שנים מקרא ואחד תרגום." It should be emphasized that all other ראשונים and אחרונים side with Rambam, and Raavan's view is completely rejected למעשה (ביאור הגר"א או"ח שם).
While space does not allow for examining all of the details of שנים מקרא ואחד תרגום, this article will attempt to show what the different views are specifically regarding what can be used for targum. One who is interested in the rest of the details of שנים מקרא ואחד תרגום should look in או"ח סימן רפה, where they are discussed fully.
When the Gemara speaks of targum (without stipulating which targum), it is assumed to be referring to the Aramaic translation for the Torah attributed to אונקלוס. This was commonly used in their time, when the Torah was actually translated into Aramaic during Kriat HaTorah. Further, the Gemara (נדרים לז: and מגילה ג.) indicates that this targum was originally given to Moshe at Har Sinai, and אונקלוס wrote it down because it was being forgotten. For all of these reasons, it is logical that תרגום אונקלוס is the ideal targum and was surely what the רבנן had in mind for the targum when שנים מקרא ואחד תרגום was first instituted. [According to Aruch HaShulchan (או"ח ריש סי' רפה), שנים מקרא ואחד תרגום was instituted in the time of Moshe, in which case תרגום אונקלוס, which was given at Sinai, was probably the only targum around]. However, the question arises today, when Aramaic is neither used during Kriat HaTorah (except for the Yemenite community) nor understood by most people, should תרגום אונקלוס be replaced by some other commentary or translation? This could depend on which of the reasons mentioned above was the reason that the רבנן selected אונקלוס for שנים מקרא ואחד תרגום. Seemingly, if the reason is based on either אונקלוס's origin from Har Sinai, there would be no way of replacing it with a new translation. If the key reason were the fact that it was used as targum during Kriat HaTorah (which we no longer do), the law would be unclear. Perhaps the fact that we no longer use it for Kriat HaTorah would open the door for us to find a replacement targum, but one could also argue that because no new translation was ever introduced for Kriat HaTorah, a new translation can also not be introduced for שנים מקרא ואחד תרגום. However, if אונקלוס was selected purely because it was written in the vernacular of that time, it could certainly be replaced by newer translations, since Aramaic is no longer a spoken language.
Rav Amram Gaon (quoted in הגהות מיימניות אות ש to הל' תפילה יג:כה) states that one must use specifically the תרגום אונקלוס, because it was given at Har Sinai. He would surely prohibit any type of modern translation or commentary, because no new translation can boast being given at Sinai. R. Yeshaya DiTrani (cited in שלטי גבורים לברכות ד: בדפי הרי"ף) mentions that there are those who believe that the point of targum is to be in the vernacular and allow one to use any foreign translation. Tosafot (ברכות שם בד"ה שנים) quote and reject this view, although they do not explicitly require that the targum used for שנים מקרא ואחד תרגום be given at Sinai, nor do they require a targum that was used for Kriat HaTorah. They prohibit replacing תרגום אונקלוס with a translation in their vernacular on the grounds that אונקלוס occasionally adds things which are not clear from the פסוקים, citing the aforementioned Gemara in Megillah where Rav Yosef states that many פסוקים could never be understood without the Targum (ועיין מעדני יום טוב על הרא"ש ברכות פרק א ס"ק ז ותפארת שמואל שם ס"ק יב). Another, more literal translation of the Torah would omit these additions. Tosafot leave unclear what the law would be for a translation of תרגום אונקלוס into another language. Since their primary objection is against the difference in content between תרגום אונקלוס and other translations, and they do not object to the idea of using a foreign language per se, one might suggest that they would permit a translation that added whatever pieces of information are added by תרגום אונקלוס.
Rosh (ברכות פרק א סי' ח) agrees with Tosafot's objection to literal translations into the vernacular but rules that one who uses פירוש התורה for targum fulfills his obligation, because it explains the text word by word. It is assumed that the פירוש to which he is referring is Rashi's commentary (see טור או"ח שם and דברי חמודות ס"ק מב). Rosh presumably believes, like Tosafot, that a targum which adds more than just the literal words is required. However, he does not require that those words of the חומש which require no explanation be read in their targum anyway. He thus permits the use of Rashi, even though Rashi has nothing to say on many simple פסוקים, because Rashi explains all words that require more than just a literal translation, and there is no requirement of targum for those words which can be understood at face value. Undoubtedly, Rosh does not permit the use of topical commentaries like Abarbanel, because he requires a targum שמפרש כל מלה ומלה, which explains word by word. Whether or not Rosh permits commentaries like Ibn Ezra, which explain all difficult words but are based on the commentator's personal understanding of פשט, would depend on whether or not he believes that the content of the targum must originate from Sinai. Rosh does not write explicitly whether or not he considers the fact that Rashi's commentary is based on traditions from Har Sinai to be an essential factor in permitting it to be used for targum, so there is no clear answer to this question. Tur (או"ח סי' רפה) rules in accordance with the opinion of his father (Rosh) but gives a slightly different reason. Whereas Rosh justifies using Rashi because it explains every word, Tur justifies it שאין כוונת התרגום אלא שיבין הענין, that the only purpose for targum is to understand the issue, implying that the criteria for a commentary to be valid for targum is that it must explain things which are unclear from פסוקים (probably by adding traditions from Sinai; see ערה"ש שם ס"ק יב). Unlike Rosh, it seems less possible according to Tur that one could justify the use of פשט commentaries, because he believes that simply explaining hard words is insufficient, and the commentary must actually help the readers understand certain ideas (which most likely means ideas of תורה שבעל פה, not the personal insights of Ibn Ezra or Rashbam). In fact, Magen Avraham (או"ח רפה ג) explains that Rashi is acceptable because "it is built on the foundation of the תלמוד." [In practice, this author has heard Rav Hershel Schachter tell someone who asked if he could use a פשט commentary for targum that he should only do so if he also reads תרגום אונקלוס.] Smag (quoted in Mordechai, ברכות פרק א סי' יט) claims that Rashi's commentary is actually better than תרגום אונקלוס for targum.
The issue of what to use for targum has remained subject to מחלוקת among later authorities, too. Rav Yosef Karo (בית יוסף או"ח שם ד"ה ואם וכ"כ בשו"ע) quotes the views of all the aforementioned Rishonim, and rules that both תרגום אונקלוס and Rashi are acceptable, and one who is a true ירא שמים will read both תרגום אונקלוס and Rashi, in order to satisfy both Rav Amram Gaon and the Smag, each of whom prefers one of תרגום אונקלוס and Rashi over the other. [It is worth noting that although Rav Amram lived before Rashi, his opinion is also the view of Ri (quoted in בית יוסף שם), who was Rashi's great-grandson, so one cannot assume that opposition to using anything besides אונקלוס for targum only existed until Rashi's commentary was written.] Rav Karo expresses no clear preference for either תרגום אונקלוס or Rashi for those who do not do both. Kaf HaChaim (או"ח סי' רפה אות כב) writes (based on Birkei Yosef) that there are Kabbalistic reasons for using specifically תרגום אונקלוס, and not Rashi, although he concludes that one who lacks access to תרגום אונקלוס can fulfill his obligation using Rashi. Aruch HaShulchan (שם ס"ק יב) rules in favor of תרגום אונקלוס even more ardently, saying that one can fulfill his obligation only with תרגום אונקלוס. He adds that this was the minhag in his time, and it should never be changed. He goes so far as to say that even if one has no access to תרגום אונקלוס, he should either wait until he can obtain a copy of it or read the text three times (which he may even mean is preferable to using Rashi). On the other hand, Rav Shlomo Luria (ים של שלמה קדושין פ"ב סי' י"ד, quoted in כף החיים סי' רפה אות כב) and Rav Shneur Zalman of Liadi, (שו"ע הרב או"ח סי' רפה סעי' ב), rule like Smag that Rashi is better than תרגום אונקלוס because it adds on more things than תרגום אונקלוס, although Rav Shneur Zalman clearly states that he considers those who recommend תרגום אונקלוס to be a valid alternative, and he, like the Shulchan Aruch, writes that one who is a true ירא שמים will read both. Rav Yisrael Meir HaCohen expresses some preference for Rashi in the Mishnah Berurah (ס"ק ה), because there are some parts of the Torah (such as much of VaYikra) which make no sense unless explained by Rashi, and in the Biur Halacha (שם), he attempts to prove that not a single גאון or ראשון explicitly writes that תרגום אונקלוס is superior to Rashi. However, his conclusion is that תרגום אונקלוס also is acceptable, because it comments on every word (whereas Rashi only comments on those words which he believes require explanation).
One additional issue discussed by Acharonim is foreign translations of Rashi. Logically, there should be no reason for the halacha to treat a translation of Rashi differently than the original (although it may be better for one who knows Hebrew to read Rashi's commentary in its original form; עיין ט"ז שם ס"ק ב). After all, the whole reason why many פוסקים consider Rashi to be a valid replacement for תרגום אונקלוס is that they do not require that targum used for שנים מקרא ואחד תרגום be written in תרגום אונקלוס's exact words and merely require a targum that explains all difficult words based on traditions from Sinai. A translation of Rashi still explains the same things that Rashi himself explains, and clearly no פוסק who permits Rashi requires the exact words of the original targum, for if he did, he would have to prohibit Rashi, too, because the original words of targum were תרגום אונקלוס. In fact, Taz (שם), Be'er Heitev (שם ס"ק ג), Machatzit HaShekel, and Mishnah Berurah (ס"ק ה) all agree that צאנה וראנה, a commentary on Chumash which is based on Rashi and is written in Yiddish, should be used by anyone who cannot understand Rashi in its original Hebrew. It seems that an English translation of Rashi would be similarly allowed based on the reasoning mentioned above.
In practice, one who uses either Rashi or אונקלוס for targum has a great number of פוסקים to rely on, and even one who finds both of these possibilities too difficult, can use an English translation of Rashi. It is a very worthwhile מצוה to perform, as it builds the habits of establishing set times to learn Torah and reviewing the weekly parsha. Aside from these positive benefits, it should be done because it is a mandatory obligation according to every Rishon (except for the rejected Raavan) and every Acharon.