The Rashbam says that they're birds, and he gives some proof or other. I remember Rabbi Menachem Liebtag suggesting that cherubs are calves, although I didn't find this suggestion on his website. I don't remember all his proofs for this, but it was part of an attempt to explain why the Jews in the desert made a golden calf, and especially why Yeravam ben Nevat made two golden calves, one on each end of his kingdom. Rashi, for some reason, only says that the cherubim have faces of babies, but neglects to comment on their bodies; maybe because it was obvious to him that they have humanoid bodies?
Wikipedia, commenting on the "Jewish view of cherubim", notes the prophecy of Yehezkel describing "the cherubim as a tetrad of living creatures, each having four faces: of a lion, an ox, an eagle, and a man. They are said to have the stature and hands of a man, the feet of a calf, and four wings. Two of the wings extended upward, meeting above and sustaining the throne of God; while the other two stretched downward and covered the creatures themselves". Wikipedia also notes that the modern academic Near East historians are convinced that cherubim have the body of a lion and the head of a man, like the mythical sphinx.
But let's be honest: we all know that cherubim are cabbages, just like seraphim are snakes and ofanim are chariot wheels. The "wings" of the cherub are obviously leaves of the cabbage. And cabbages certainly make fearful guardians of the Garden of Eden, at least when they are wielding a revolving sword.