After Avraham takes leave of Avimelech and forgives him for having taken Sarah, he davens on Avimelech's behalf. The Torah in Parshas VaYeira then tells us that Hashem remembered Sarah and she gave birth to Yitzchak. Chazal see a causal connection between these two parshiyos. It was because Avraham davened on Avimelech's behalf so that Avimelech should have children that Avraham in turn was blessed with children himself. From here we learn the principle that one who davens for someone else's needs will in turn have his own needs provided for by Hashem.
R' Yechiel Michel Feinstein is bothered by this reading of causality into the parsha. The opening of Parshas Vayeira tells the story of the angels who visited Sarah and told her that she would give birth to a son one year later. Hashem had previously made the same promise to Avraham. Yitzchak's birth was preordained -- whether or not Avraham davened for Avimelech seems irrelevant.
From the fact that Chazal do see Avraham's tefilah as crucial, we see a tremendous yesod: Even though something may be promised and preordained, it still requires the added ingredient of tefilah to bring it to fruition.
We see this in Parshas Toldos as well. "Va'ye'etar Yitzchak," Yitzchak davened with great intensity that he and Rivka should have children. Wasn't Yitzchak the recipient of the bracha given to Avraham Avinu that guaranteed that Klal Yisrael would emerge from his progeny? "Why the need for such intense tefilah?" asks the Seforno -- Yitzchak's having children was a sure thing?! The answer once again is that brachos and nevuah are not sufficient so long as tefilah is missing (I read the Seforno as making two points -- Yitzchak was davening for children and for those children to come through Rivka, not just the latter point).
Commenting on, "V'Yitein lecha Elokim m'tal hashamayim," Rashi writes that the bracha should be given to Ya'akov "b'din," i.e. it should be something Ya'akov deserved based on merit. The Shem m'Shmuel asks: If Ya'akov deserved the rewards based on his own merit, what does he need the bracha for? I think the answer yet again is that even if Ya'akov deserved to receive "m'tal ha'shamayim u'mishmanrei ha'aretz," without Yitzchak's tefilah/bracha that reward might not become a reality.