Why is a ketone not capable of hydrogen bonding among themselves? The ketone has one oxygen atom in it and there are two lone pairs hanging out, both of which make it seemingly capable of hydrogen bonding. But in reality it is not.

Did some research and found this on chemguide:


  In methoxymethane, the lone pairs on the oxygen are still there, but the hydrogens aren't sufficiently δ+ for hydrogen bonds to form. Except in some rather unusual cases, the hydrogen atom has to be attached directly to the very electronegative element for hydrogen bonding to occur.


Based on the info, I am assuming that the carbon atom in carbonyl group is not electronegative enough to give a partial charge large enough for hydrogen bonding to the hydrogen atoms, say in pentanone.
Short answer: the ketone oxygen can participate in hydrogen bonding

The compound you mention, methoxymethane, is an ether not a ketone.  



Ethers don't hydrogen bond very well because the oxygen isn't very polarized.  

On the other hand, the carbonyl in a ketone is polarized.  We can draw resonance structures that show this polarization.



(image source)

The negative polarization on the carbonyl oxygen allows it to play the role of hydrogen bond acceptor as illustrated in the following drawing.



(image source)

Edit: If you are asking if the hydrogens on the carbon adjacent to the carbonyl carbon (or any other carbon in the backbone of a simple ketone) can participate as the donor in a hydrogen bond, then the answer to this question is "no". These $\ce{C-H}$ bonds are typically less  acidic and less polar than the $\ce{O-H}$ bond in water.

Therefore, while the oxygen in pentanone can participate in hydrogen bonding with donor hydrogens in other molecules, the hydrogens in pentanone cannot participate in hydrogen bonding.  Pentanone cannot hydrogen bond with itself.