Targum Yonasan: In the first half of his dream, the three branches represented a. the three Avos, ¹ Avraham, Yitzchak and Yaakov, whose children were destined to slave in cement and bricks and all kinds of hard work in the fields; ² and b. the three redeemers (Moshe, Aharon and Miriam). ³ In the second half, his squeezing out the grapes into the cup of Pharaoh represented the cup of punishment that Pharaoh would ultimately be made to drink. And the favorable interpretation was a reward for the favorable dream that he had dreamt about Yisrael.

Moshav Zekenim (to 40:19): A vine has roots and lasts - this shows that the butler will survive and be strengthened. The baker saw baked goods; even if one puts them in a storehouse, they spoil and deteriorate by themselves, so Yosef understood that he will not survive.

Ramban: Refer to 40:10:1:2**.

Tosfos ha'Shalem (1, citing Moshav Zekenim): Surely the sheaves must represent years. There cannot be seven days of famine, followed by seven days of satiation! However, perhaps the three branches in this dream should mean three years? It seems that Yosef did not know this through Nevu'ah, for Berachos 55a learns from here that dreams are fulfilled like the interpretation! Perhaps Yosef knew that in three days' time would be Pharaoh's birthday, and every year he judges on his birthday.

Gur Aryeh: Were the dream to mean that he would be re-instated in three years, he would have seen three separate vines (since the yield of each year is a separate entity). Rather, he saw three branches on one vine, which means three units within one year. The agricultural year is a solar cycle, and the only other solar unit is the 24-hour day. (The month, on the other hand, is a lunar cycle, while the week is not indicated by the luminaries at all. ¹ )