Chazal derive from the pasuk in parshas Eikev, "Mah Hashem... shoel m'imach ki im l'yirah," that everything is in the hands of heaven except yiras shamayim (Kesubos 30). This is the one area where we are free to exercise our bechira chofshis, our free will. By coincidence the daf hayomi for this past Shabbos touched on this topicas well. The gemara (Brachos 10a) relates that there were some evil troublemakers who lived in R' Meir's neighborhood so he davened that they should die. When Bruria, his wife, heard what he was doing, she stopped him. Instead of praying for their death, she said to her husband, he should daven that they do teshuvah. The Maharasha asks how R' Meir could ask Hashem to cause people to do teshuvah -- isn't the choice of whether to do teshuvah, whether to have yiras shamayim, the one area where Hashem does not interfere with people's free will? The simple answer (Maharasha just says "yesh l'yasheiv" but doesn't offer an answer) is that R' Meir meant that Hashem should put these bad guys in a situation where it would be easier for them to make the right choices. In other words, Bruria was making a typical liberal argument: If only these rebellious youths were given a support structure and the proper environment, they would not be such bad guys. It's an easy answer, but I don't think it fits the language of the gemara very well. See Michtav m'Eliyahu vol 3 for another approach.
There are a range of views as to the scope of what is included in, "hakol b'ydei shamayim," except yirah. The Rambam in Shmoneh Perakim takes an expansive view of free will and includes under the heading of yirah any decision that has moral or religious implications. Who you should marry, how you make your money, etc. all impact on mitzvos in some way (there is a mitzvah to get married, there is an issur of gezel) and therefore fall under the heading of yirah and are subject to free will. At the other extreme is the position of the Ishbitzer, who writes in a number of places that in truth even yirah itself is dictated by G-d and the gemara simply is telling us what we can tell is controlled by Hashem given our limited human frame of reference. Between these extremes are other positions, such as R' Dessler in Michtav who limits bechira to a single focal point that rises and falls with man's level of religious committment.
The Rambam (Hil Teshuvah ch 5) asks how we can reconcile G-d's foreknowledge of future events with our free will. If G-d knows what is going to happen, doesn't that mean our choices are already determined? The Rambam answers by quoting the words of the Navi, "Lo machshivosei machshivoseichem," G-d's knowledge is not like human knowledge. The clash between foreknowledge and free will is only a problem within our limited human frame of reference, but not from G-d's transcendent perspective.
Ra'avad sharply critiques both the Rambam's question and his answer. He charges that the Rambam's answer is no answer at all -- it just avoids the question by saying it is outside the boundaries of our comprehension. If the Rambam did not have an answer, says the Ra'avad, he should not have raised the issue in the first place. The Ra'avad then offers his own answer, that Hashem, "hei'sir zu ha'memshala m'yado u'mesarah b'yad ha'adam atzmo," He circumscribed his own power and turned this area of free will over to man. Hashem's knowledge is no different than an astrologer who may know the future, but whose knowledge does not have an impact on events themselves.
R' Ahron Soloveitchik (in Perach Mateh Aharon) teases an interesting lomdus out of the language of the Rambam and Ra'avad. The Ra'avad understands free will to be a function of, "hei'sir zu ha'memshala," of Hashem withdrawing his control. Not so the Rambam, who is unwilling to set any limits on Hashem's authority and is therefore forced into trying to come to grips with the head-on collision of free will vs. Hashem's knowledge.
It's not relevant to Parshas Eikev, but while on this topic I can't resist posting an amazing vort of the Oheiv Yisrael, R' Avraham Yehoshua Heschel, on Parshas Toldos. Rikva felt kicking in her womb when she passed houses of avodah zarah worship; she felt kicking in her womb when she passed the beis medrash. She says, "Lamah zeh anochi?" and goes to seek the advice of a Navi. What troubled Rikva so much? The Oheiv Yisrael writes that Rikva thought she had one child in her womb. Every person, even a child, has to make certain choices. One person may choose to follow his heart to a house of avodah zarah; another person may choose to follow his heart into the beis medrash -- but we each must choose. Bechira chofshis is not just about how we behave -- it's about how we define ourselves, our sense of identity, our sense of self. Bechira is not about what you do -- it's about who you are. When Rivka felt what she thought was the same child kicking for both the beis medrash and the beis avodah zarah, she thought this child could not choose a path; she though this baby had no identity, no sense of self. "Lamah zeh Anochi?" -- "Where is the sense of 'I' that defines who this child is?"
The gift of bechira means that we are afforded the opportunity to define just who the "I" inside each of us is. Let's hope we choose wisely.