There are three main theories. One popular is that he is some random individual, possibly a member of the Night’s Watch who disappeared in a ranging. The fact that he calls Samwell “brother” (III: 536) seems to support the general idea, at least, that Coldhands was a member of the Watch. However, many find the unknown nature of this brother of the Watch to be a major strike against the theory. Another theory is that he might actually be the "last hero" (I: 203), which has interesting implications but many find too esoteric.
The most popular theory is that he is in fact Benjen Stark. It’s believed that he is now an agent for the children of the forest. Coldhands’ appearance—black hands like the wights that the Others make (III: 536)— may indicate that he was in fact turned into a wight by the Others, but that the children intervened and wrested him away from the control of Others. The chief strikes against this are that Samwell’s thoughts after leaving Bran with Coldhands do not suggest that Bran recognized his uncle, Leaf suggests to Bran that Coldhands died "long ago" (V: 175), and there is a description of his eyes being black in color (V: 69). This may be explained by the fact that he could look quite different from how he looked when alive, although the change in eyecolor to black (rather than, say, the icy blue of the wights, is inexplicable). This may instead give weight to the idea that he is in fact the last hero, or perhaps someone as yet unknown, whose identity may not even have any particular importance.