- Jacob was struggling with Esau's spirit. According to Midrash (Genesis Rabbah 77:3) and Rashi (commentary on Genesis 32:25), the spirit (read: guardian angel) of Esau was attempting to weaken Jacob before the encounter the following morning (Nechama Leibowitz). This interpretation does not make sense because why would Esau bless Jacob with a new name?
- Jacob was struggling with an angel. This is the most common depiction of the account. Although the term איש is used ("man"; Genesis 32:25), a term used for "angel" (אלהים) is used later in the passage (v. 29, 31), much like we see in other passages (Hosea 12:3-4; Judges 13:17-18).
- Jacob was struggling with G-d. Although Jacob could have struggled with an angel, I think the theory that the struggle was with G-d works better for a couple reasons, aside from the fact that אלהים is also one of the names of G-d. One, after the wrestling, Jacob named the place (Genesis 32:31) where the incident occurred פניאל, which means "I have seen the face of G-d (פנים אל פנים) and survived." The theme of being "face-to-face with G-d" can also be found in text during the Burning Bush narrative (Exodus 3:6). Two, Jacob's new name, Israel, means "he who struggles with G-d." The downside of this argument is that G-d is incorporeal. In the Guide for the Perplexed (II, xlviii), Rambam points out that because of G-d's Infinite Oneness, anything describing to G-d needs to be figurative, which means that Jacob was not literally wrestling with G-d.
- Jacob was struggling with himself. In Genesis 32:25, the text does state ויותר יעקב לבדו ("Jacob was left alone"), so the most obvious answer would be that Jacob was alone. It is a possibility that this struggle was in the form of prophecy, as Rambam opined (Guide for the Perplexed, II, xlii), but if Jacob was temporarily in a state of solitude, odds are that Jacob was wrestling with his conscience. This was a paramount fight between his good and evil inclinations.
In my humble opinion, the most compelling answer is a combination of #3 and #4. Although the identity of the "antagonist" has some bearing, what is even more important is the end result of the occurrence. Jacob was not only dealing with the angst of seeing his brother after so many years, but also how it all ties together within the greater context of G-d. Jacob outgrew the negative connotations of his previous name. No longer did he have to deceive his father, run away from Esau after stealing his birthright, or avoid the confrontation that took place between him and Laban. No more deceit or manipulation. No more running. No more hiding.
In spite of having his sciatic nerve harmed in the process, Jacob was considered to have been שלם (Genesis 33:18), which can mean "safe," but also means "whole" or "complete." It has the same root as the word שלום (peace), meaning that Jacob was finally at peace with himself. That night, Jacob was his own opponent. What did Jacob accomplish that night? He reconciled his sordid past with the fact that he can change and feel a sense of renewal in his life. In short, he accepted all aspects of his humanity.