See here for a rundown of the basic opinions.
1) Rashi, the Ibn Ezra and the Ramban all speak about it being an angel that Hashem sends as His messenger to do things like provide blessings, redemption, etc. The Ibn Ezra (in Shemos 23) specifically identifies the angel as Michoel.
2) The kabbalistic understanding (brought in the Or Hachaim on the passuk) is that it refers to Hashem's presence, not an angel as a separate being. So it is saying that the Shechina should bless.
3) The Malbim that says that this refers to protection in exile, where he was speaking in exile in Egypt where Hashem's presence would not be felt in a revealed way, he is asking that the blessing through more natural, hidden means should accompany them in exile.
Additionally, the Kehot Chumash interpolated translation brings an interesting reading, that I have never seen explicitly (and their own footnotes don't source it), but it reads this verse with the preceding one as one unit, like this:
15 He blessed Joseph and said, "May God, before whom my fathers Abraham and Isaac walked, the God who has been my shepherd from my earliest days until this day,
16 and has always sent me the angel who delivers me from all harm, bless the lads.
The bold is the translation of the actual words, the not bold is the interpolation. According to that reading (which fits very nicely with the Or Hachaim in the sense that the Or Hachaim wouldn't add the interpolated words, but would see the "Malach" as a continuation of the previous two mentions of "Elokim" in the previous verse all referring to some aspect of G-d), and certainly doesn't contradict Rashi or the Ibn Ezra (I don't remember the Ramban)), the angel isn't asked to bless at all, the Sender of the angel is.