Often, we just use hydrogen for this! Metals like palladium can work some real magic doing the heavy lifting here. Process chemists hate hydrogen gas, though, and rightly so - everyone knows about its tendency to explode. It's worse, though - most hydrocarbons have a flammable range of about 1-8% in air - any more, and there's just not enough oxygen to support combustion. Any less, and you don't get enough heat to keep the reaction going. Hydrogen, however, starts a little higher, about 4%, and is still flammable in air up to a whopping 75%! The stuff's dangerous.
Fortunately, palladium can rip a hydrogen off of just about anything and move it to something else, as long as it's energetically "downhill." When you're not using hydrogen, it's called transfer hydrogenation. Cyclohexadiene, if it gives up a couple hydrogens, becomes benzene, downhill by nearly 6 kcals!
Often, this will suffice for a hydrogenation. Something a bench chemist runs at work will likely use hydrogen on the first go (although we use transfer hydrogenation at the bench sometimes!) because it works well. Unfortunately, you have to run it at high pressure in a vessel unsettlingly named a "bomb," and the process guys tend not to like bombs. Transfer hydrogenation will get a close look.
This is not to say that it's never used. In fact, using dihydrogen for hydrogenation at the process scale is often unavoidable (you don't want benzene in your cooking oil, or drugs!). Your Crisco and trans fats are products of a gaseous hydrogenation process.
Please correct me on any of this, process chemists, it's a big day when I work at 10 gram scales.
Once again, benzene resonance makes tings somewhat easier.
Formate has a better equivalent weight, is ever so cheap, and doesn't smell bad. Aldrich sells 1,3-cyclohexadiene 100 ml/$(USD)534.00 (1.02 moles net). Price a Parr bomb and a tank of hydrogen.
Do you Greenly recycle the benzene back to cyclohexadiene? "8^>)
We do this reaction in my Organic Chem labs. But, instead of cyclohexadiene, we use cyclohexene. It works great. The existence of cylcohexadiene in the reaction mixture is fleeting, I'm sure. Thermodynamics and aromaticity are just two of the many concepts we can talk about from this lab.
In my lab, we polymerize this stuff to produce poly-(1,3 cyclohexadiene). It is a classical monomer for anionic polymerization, You can do nice copolymers with butadiene, isoprene and styrene...