(seems I'm perpetually responding on this subject.. oh well, here goes)
As Academic here said, chemistry is essentially quantum-mechanical. Or at least the fundamentals of it, such as chemical bonding and reactivity. So quantum mechanics certainly has an important role in biochemistry. But on the other hand, it is the same role that it has in the rest of chemistry. Photosynthesis, for instance, involves absorption of light by matter - which is a quantum mechanical process, and it also involves things like the transfer of electrons, which is also a quantum mechanical process. But these processes are of course not at all unique to biochemistry, or even chemistry itself, so it's not a surprise, exactly.
If the question is: "Is quantum mechanics significant to biological/biochemical processes in such a way that biochemists need to learn quantum mechanics [more than any other chemist]?"
The answer most in the field would give to that is simply "No."
As it stands right now, biochemists know
less quantum stuff than most chemists, (I'm not knocking 'em for it) as they're the farthest removed from these 'fundamentals' where QM is involved, i.e. reactions and bonding and such. They focus rather on the bigger things which are specific to biochemistry, such as protein structure and function, genetics and such. Whereas studying light absorption in photosynthesis (for instance) is better left to physical chemists, chemical physicists, and quantum chemists, who have more detailed knowledge on light-matter interactions in chemistry.
So one must distinguish biochemistry and other diciplines, even though the other diciplines might be studying biochemical systems! The reason why the answer to the question above was 'no' is because once you reach the 'biochemical' level, quantum mechanical effects are no longer in play. E.g. you don't need quantum mechanics to figure out gene regulation, or protein folding, or what a protein does in a cell. But you may need quantum mechanics to fully understand
how it does it, but it's the same for any chemical reaction. (and the more you 'zoom in', the more quantum mechanical it becomes)
lmerriam said:
I've only seen some other (speculative) involving quantum "spin" and bird migration.
This isn't really speculative. Some birds do have magnetoreception, they're pretty sure.
Since cells communicate chemically, you need something that reacts to magnetic fields strongly enough to affect chemistry.
The only thing that could be (given that we haven't found any tiny induction coils in cells) is molecules with a net electronic spin. This is quite unusual, because spin seldom plays such a direct role in chemistry and (equivalently) little chemistry is affected by magnetic fields.
(However there
is unfortunately a lot of speculative nonsense out there in this realm. Which is why, even though I do quantum-chemical studies of biochemical systems, I don't use the term 'quantum biology' and don't like it. I think it implies quantum effects of macroscopic significance within bio systems, which is something not generally believed to exist.)