Rashi (on Bereshis 37:3) quotes Midrashic sources that Yaakov favored Yosef either because Yaakov taught Yosef all that Yaakov had learned in the Yeshiva of Shem and Ever, or because Yosef's appearance was similar to that of Yaakov. These reasons need some elaboration, as neither one would seem to be a likely basis for favoritism.

It may be suggested that Yaakov believed that one son had to be chosen to be the next leader of Bnei Yisroel, as was the case with his father Yitzchak and himself. Yaakov did not want to engender a repeat of his own experience with Eisav, in which the brothers had to vie for the leadership role, while their father was no longer in a position to firmly establish it. Thus, Yaakov felt that by hand-picking his successor, he would avoid such a clash within his own family.

This explains the reasons advanced by the Midrash and Rashi for Yaakov's actions. Yaakov realized that leadership of the Jewish People was largely determined by passing down the Mesorah (Tradition) of Torah. Torah study was Yaakov's primary occupation in his youth (v. Rashi on Bereshis 25:27, from Midrash), and he perceived that his commitment to and mastery of the Mesorah was a primary factor in his succession of Yitzchak. Thus, Yosef - who was Yaakov's closest disciple - was thereby viewed as uniquely qualified to be the next leader.

Rashi (on Bereshis 25:19) quotes a Midrash that Yitzchak's appearance was akin to that of Avrohom. Yaakov may have interpreted this as a sign that Yitzchak was an extension of Avrohom and was thus designated by Hashem as Avrohom's successor. (The Midrash [v. Rashi ibid.] comments that Lot, too, looked like Avrohom, and some explain that Avrohom believed that Lot was to be the bearer of Avrohom's message, prior to Lot's corruption). This explains why Yosef, who very much resembled Yaakov, may have been viewed by Yaakov as the son whom Hashem designated as the successor in leadership.  

The special robe which Yaakov fashioned for Yosef was a garment of royalty, and it implied a position of leadership. This is precisely why Yaakov made the robe, as it furthered his device to appoint Yosef as the next leader, in order to avoid a clash at the end of Yaakov's life.

The suggestion that Yaakov's special treatment of Yosef was geared toward appointing Yosef as Yaakov's successor sheds light on a perplexing comment of Rashi (on Bereshis 37:11), where Rashi explains that Yaakov awaited the time that Yoesf's kin would bow down to him as a ruler, as foretold in Yosef's dreams. Although the brothers interpreted Yosef's dreams as signs of haughtiness, Yaakov felt that the establishment of Yosef as ruler was the best approach, and he had no reservations about the dreams' fruition; on the contrary, Yaakov was confident that the dreams were a forecast of Yaakov's success in establishing Yosef as the next Jewish leader.