This is a tricky question to ask correctly. One attempt has already been closed as subjective and argumentative. There is no one correct answer, for sure. However, there are interesting reasons that I believe are worth recording here.
Ideally include supporting documentation/research. I will vote up for quality of answer, not based on whether I agree with the answer.
I read in an issue of a mountain bike magazine (sorry I can't remember the issue or even the magazine), that helmets afford somewhat limited protection. That is not to say that you shouldn't wear a helmet.
The study showed that helmets can worsen head injury in crashes involving torque to the brain (i.e. rotational injury). Rotational injury is not like the relatively benign bleeding from simply a scraped scalp (though no head injury should be taken lightly!). Since the brain is not perfectly round but elongated, rotation can happen more easily at a pivot point. Torque injuries are the source of the most serious brain injuries.
Also the study seemed to suggest that helmets are most effective at protecting you in high speed crashes and crashes into sharp objects, which is particularly important in mountain biking. At medium to low speed crashes, the helmet's effectiveness was in doubt.
Other non-mountain bike specific studies seem to have shown the frequency of head injuries compared to other types of injuries is rare. The statistics can matter in deciding if helmets should be mandatory because if you also have comparable amount of spinal injuries then you could argue that it should be law to wear back braces like those DH mountain bikers wear, even on the road! As a consequence, it is understandable why some people think helmets are an arbitrary requirement.
But those studies also need to take into account in what environment these injuries take place. E.g. in Amsterdam and most European countries no one wears helmets but bicycles and cars move much slower and because of their infrastructure they do not have to meddle with cars as much. It's a different story in places like USA and Australia where there is little or no separation between bicycles and cars, and cars move very fast.
Anyway I always wear a helmet.
Nobody has mentioned on the Against side:
Noise - I have tried many helmets, and above a reasonable pace, all of them have wind noise, which helps to drown out the sound of big metal things aiming towards me.
I always where one when riding an MTB in a forest downhill, but on my commute I find I am much happier hearing traffic behind me so I can take evasive action, rather than being surprised by it as it comes alongside!
I've already fell into the ground, and I'm lucky I was wearing a helmet. I do know the impact, and I say to everybody: it's better, it's safer, it's necessary to wear helmets.
People say helmets are ugly, but I think an bleeding head is uglier.
For on my racing bike : I always wear a helmet by principle on my racing bike and once crashed really hard on top of my head with my racing bike and I was really glad I wore a helmet. The only person in our cycling group not wearing a helmet was so impressed he finally bought himself an helmet.