Many of the replies in this thread are wrong!
acetone contains an oxygen with two lone pairs and hence can act as a hydrogen bond acceptor. Since it does not contain an electronegtive element (O,F, N) bound to a hydrogen, it cannot act as a hydrogen bond donor. Since it is only capable of being a hydrogen bond acceptor, it would not be capable of hydrogen bonding with itself. However, in solution, it could hydrogen bond with water since water contains a O-H bond.
Soooooooooo, acetone is capable of hydrogen bonding so long as the other party is a hydrogen bond donor.
Hope that helps!