ואמר רבי חנינא הכל בידי שמים חוץ מיראת שמים
And Rabbi Chanina said: Everything is in the hands of Heaven, except for the fear of Heaven.
According to this Talmudic passage, the only choice we have is whether we have the free will to serve G-d out of fear (יראת), based on Deuteronomy 10:12. The first issue I have here is that יראת is commonly translated as "fear," although a closer translation would be along the lines of "reverence" or "awe." The second issue is that if you look at the rest of the verse in Deuteronomy, it ends with "loving Him and serving Him with all your heart and all your soul." While I don't deny the importance of having a sense of awe about G-d, I find that love needs to be the ultimate goal in one's spiritual practice.
If taken literally, this passage severely limits the idea of free will. Although I believe that belief in G-d has the potential to change one's behavioralism, fear in Heaven is not the only factor in one's free will. Free will extends well beyond a reaction to one's perception of G-d. This verse seems to conclude that "serving G-d" guarantees good behavior, and after observing enough people and looking at enough history, I know that is certainly not the case.
On the other hand, I know that the Talmudic rabbis were known for using literary devices, particularly hyperbole, to make a point. The rabbinic literature teaches us there are multiple mitzvahs that are so important that following them is as if the entirety of Torah were fulfilled. Those included, but were not limited to, tzedakah (Bava Batra 9a), not speaking lashon hara (Tosefta, Peah 1:2), wearing tzitzit (Menachot 43b), and circumcision (Nedarim 32a). A strictly literal reading not only contradicts many Jewish teachings, but also common sense. I will assume that Rabbi Chanina was using a literary device to emphasize the importance of recognizing the "fear of Heaven." From what I can gather, what Rabbi Chanina was trying to convey is that the choice that ultimately matters is how the aforementioned reverence for G-d affects our behavior.