In what sort of Sukos did Hashem house Yisrael in the desert?
Rashi (citing Targum Onkelos). Ramban #1 and Targum Yonasan: "Sukos" refers to the protective Clouds of Glory. 1
Ramban #2 and Rashbam: In (wooden) huts. 2
Ramban: As the Navi indicates in Yeshayah, 4:5 & 6. See Ramban who elaborates. See also K'li Yakar, who comments that had the Pasuk referred to huts, it ought to have written "Ki ba'Sukos Yashvu B'nei Yisrael ba'Sukos ... ". A further proof lies in the fact that Bil'am referred to "the tents of Ya'akov" (Bamidbar 24:5) - and not to 'the huts'.
Presumably, the miracle that we commemorate lay in the fact that they found enough wood in the desert to built huts for a few million people. The two opinions are actuaally those of R. Eliezer (Ananei Kavod) and R. Akiva in Sukah (huts) in SUkah, 11b.
Why do we commemorate the Clouds of Glory but not the Manna or the well of water?
Oznayim la'Torah: Because, since the Torah - in Bo, Shmos, 12: 42 - refers to Yisrael in the desert as "Tziv'os Hashem", a King is duty-bound to feed his troops, and it is not something that calls for commemoration. Not so, when he bestows upon them honor in ways that are not obligatory.
Why does the Torah insert the phrase "Ani Hashem Elokeichem"?
Seforno: To teach us that all the above Mitzvos are to spread His Divineness over us, in that He will never avert His Eyes from us.
What is the underlying reason behind the Mitzvah of Sukah, as hinted in the current Pasuk?
Ramban: It is a reminder that, during the entire period that they spent in the desert, they never entered a house or an inhabited location - but lived under the Divine protetion of the Ananei Kavod. 1
Rashbam: 'When you gather the produce from your granary and wine and olive-press into your houses, 2 and your houses are now full of grain, wine and oil, remember how, in the desert, for forty years, Hashem housed you in huts, 3 where were had nowhere to settle and you owned no property, and thank Hashem for your current situation'.
Hadar Zekenim (on Pasuk 40): In the event that in the judgment of Yom Kipur, Yisrael were sentenced to Galus they now move out from their houses to the Sukah, and it is considered as if the decree of Galus has been fulfilled. 4
Sifra: The fact that the Torah adds "asher Hotzeisi eschem me'Eretz Mitzrayim" is an indication that the Sukah is to commemorate the Exodus from Egypt. 5
Oznayim la'Torah: It cannot be a reason for the Mitzvah, since the states in Sanhedrin, 21b that the Torah gave reasons for only two Mitzvos - and this is not one of them. It must therefore mean that although one is not obligated to think about the background of the Mitzvah whilst performing it, one is obligated to do so by the Mitzvah of Sukah - and the same applies to Tzitzis and Tefilin. See Oznayim la'Torah DH 'Lema'an Yeid'u' #1.
Rashbam: See Devarim 15:13.
And it is to remind us of this that we leave our house and move into the Sukah for seven days.
Refe also to 23:39:0.1:1.
See Torah Temimah, note 174.
Why is "Doroseichem" written Chaser (without a Vav)?
Hadar Zekenim (on Pasuk 21): It can be read 'Diraschem', to hint that one dwells in the Sukah like in one's Dirah (house).