Many Generations

Rashi: "Remember the days of old", what G‑d did to past generations who provoked Him to anger

"Reflect upon the years of [other] generations"
[i.e.] the generation of Enosh, whom [G‑d] inundated with the waters of the ocean, and the generation of the Flood, whom He washed away. Another explanation is: If you have not set your attention to the past, then "reflect upon the years of generations," i.e. to recognize the future, that He has the power to bestow good upon you and to give you as an inheritance the days of the Moshiach and the world-to-come.

"Ask your father"
These are the prophets who are called ‘fathers,’ as Scripture states regarding [Elisha’s crying out to] Elijah, "My father, my father, the chariot of Israel!" (II Kings 2:12)

"your elders": These are the Sages.
"and they will inform you": of the events of the former times.

Baal HaTurim: This verse mentions 3 generations. Juxtaposed to this is "When He bestowed heritage." This hints that whenever a person, his son, and his grandson are Torah scholars, it is for him as a heritage that has no end.

Ramban: "ask your father"
hints to those who understand the events of former days, and your elders also hints to those who understand the past...The meaning of "remember the days of old" is that they apply their hearts to remember the 6 days of Creation, the good He did for them at the time of the formation of the nations, and that they contemplate in order to know what was done for them during the generations since the Shechinah dwelled among them.

Ohr HaChayim: "remember the days of old"
hint to the 6 days of Creation, when G‑d manifested himself as extremely active. "Who has made you" which Moses describes as the supreme improvement G‑d made in the condition of man since the sin of the Garden of Eden when He granted the Jewish people access to His Shechinah on a regular basis. Moses now says "ask your father and he will tell you," hinting to the prophets whom G‑d provided for us to consult with.

Tzeror HaMor: "remember some history"
G‑d's benevolent activities extend not only to Israel but globally from the time the universe was created. He provided generously for all various species on earth. "Ask your father" to instruct you on how to learn history by reading the Torah carefully. Failing this, if you do not have a father, "ask your elders and they will tell you"

Maggid Mesharim: "remember the days of old"
refers to the Shemitah year when the Holy Side reigned; "reflect the years of generation after generation" refers to the reign preceding the one of holiness. One must explain "ask your father and he will tell you." "When the Supreme One gave the nations their inheritance" and "For G‑d's portion is His people." means that their souls are from the internal ones, and the kelipot/shells have no part in them.

Chidushei Harim: "reflect upon the years of each generation"
Heaven grants each generation, each historical era, a new outlook and perspective on the Torah, a new insight that is in tune with the spiritual climate of that generation. The spiritual leaders are sensitive to the particular needs and problems that confront the young people of their generation. They bring the Torah to life, interpreting its words in terms of the current trends, satisfying the young generations' spiritual hunger.
"the years of each generation"
every single year unfolds a new energy and a unique freshness to each person's perceptions. The word "shanot" means years but can also mean shinui/change or shoneh/different. The word shanah/year derives from shinui and shoneh, from changes and differences.

Kenesset Yechezkel: Reflect that sometimes an entire generation must return in a collective reincarnation to receive another opportunity to fix something the generation missed implementing the first time around. (Peninei HaHassidut)

Ohr Elimelech: "Ask your father, and he will tell you"
every single person can turn to G‑d because He is our parent. No matter how unevolved the state of one's mind, one can always ask from wherever one's consciousness happens to be, like a child asking a loving parent. In response to such innocent asking, G‑d will answer the person in a way he or she can understand.

Mei HaShiloach: "remember on days of old"
means all that is written in the beginning of the Torah, until the words "and the heavens and the earth were finished."
"Reflect the years of many generations"
means the 2 parashot of Bereishit and Noah, which include the 10 generations from Adam to Noah, and then the 10 generations from Noah to Abraham. What is to be reflected on is the way the blessed G‑d dealt with the 20 [evil] generations.
"Ask your father and he will tell you"
means to study the events of Abraham's life, as told in parashot Lech Lecha, Vayera and Chayei Sara.
"Your elders and they will say to you"
means the events of Isaac and Jacob, meaning the parashot of the rest of Genesis, to understand all the great dealings and spiritual exchange the blessed G‑d had with the patriarchs.

Lubavitcher Rebbe: The Torah teaches that a person "ask your father" about "one generation and another"
namely about the days of Mashiach and the world to come. (see Rashi on: "and he will tell you") Here we see that a father should educate a child about Mashiach, and not let the child pick up the knowledge by himself. Even though the concept of Mashiach is quite lofty, it is one of our principles of faith which needs to be taught to children even at a young age. With a child we stress the fact that with the coming of Mashiach, "delicacies will be as plentiful as dust, " (Rambam), as this is something a kid can relate to easily. When the child matures, so too will his perception of Mashiach. When they are still young, a child should be taught to cry out earnestly and enthusiastically, "we want Mashiach now!"

Zohar Ha'azinu 298:
"Remember the days of old, consider the years of many generations…." Remember the days of [the] old [world]. Rabbi Aba said, What are the days of the world? They are the six days with which G‑d, created the world, as written, "for six days G‑d made heaven and earth," (Ex. 31:17) rather than "in six days". We have already explained it. "Consider the years of many generations" means that the days of the world will be known and acknowledged by all these years and days, and each and every generation to the generation in which you live.

"Ask your father, and he will recount it to you" (Deut. 32:7) is referring to G‑d. This is the meaning of, "is not He your father that bought you?" (Ibid. 32:6) "And he will recount it to you" means that He will disclose to you depth of wisdom. What is it? When the six days comprehended the world, they did so only for your sake that you will come and be occupied in Torah. As we have learned, whatever G‑d did, He did on the condition that Israel will appear. If they will receive the Torah, good. Otherwise, the world will return to chaos. For this reason, the days of the world knew and realized everything.