What's funny is that while people have speculated a LOT about the "half-blood" bit, everybody is leaving the "prince" bit open to interpretation and revelation.
But let's say we fixate on the 'prince' bit. Since "half-blood" accompanies the word, one is seriously inclined to think Tom Riddle is the prince. But let's say that it isn't Tom Riddle, and the "half-blood" bit refers to the nature of the prince, not what he is the prince of. If this is the case, then we can safely dissociate the two phrases and use "half-blood" merely as the criteria for ruling out possibilities.
Now, Dumbledore is a master of magic, so one could associate the term 'prince' with him, although he isn't exactly evocative of the image of a prince, purely due to his age. However, it would be interested as to whether or not he is half-blood. Anybody know?
Hagrid could be considered a prince of monsters, due to his giant heritage (and hence half-blood). It is unlikely that it is Hagrid, though, since the giant storyline appears too minor to be central to the plot. Also, the giant storyline is shared by that other lady, so that further decreases the likelihood of it being Hagger.
Crookshanks is, of course, a possible, but not very probable, choice. He (she? if she, then not) is very intelligent, determined (as with his attempts at the destruction of Scabbers), though these could be said to be traits of cats in general. Another thing is what he is a prince of. You could do the whole morph thing, but that's a bit trite and cliched with Rita, McGonagall and Petigrew doing that.
Ron is pureblood Hermione is female and muggle (in the sense of having no magical bloodlines). There's Dumbledore's brother, of course. You could run the whole mysterious stranger thing. Again, a bit cliched.
I think it's Tom Riddle, myself. The chamber of secrets is, after all, almost like a prize, a inheritance.