I saw people here saying they use headgear (and it is found in many gyms). But as far as science can go, they only protect the skin of the head and not the brain (which takes longer to recover, if...).
That's the thinking behind the current international amateur boxing authorities ruling that men's amateur fights are now to be conducted without headguards, for some reason they haven't stopped the use of headguards for women though. The brain will rattle around inside the skull whether or not a headguard is used. It's the brain hitting the skull that causes the bruising which of course is bleeding. The amount of bruising/bleeding depends on the blow received obviously but it's been shown in medical studies that even small blows overtime if repeated cause brain damage. It's been shown in footballers ( soccer) who head the ball a lot, especially in the 'old days' when the ball was a much heavier, thicker leather one which got even heavier in the wet.
One of the problems in boxing, MMA (as well as kickboxing, MT etc) and horse racing is that the participants in these cut weight, often causing dehydration. Jockey's especially cut weight permanently as they are always cutting, they have to weight the same at the end of the race as they do at the beginning, they will typically have up to ten rides a day plus riding out. Boxers and other fighters at least can eat and rink after the weigh in, on same days weigh ins which are common in the sections below the top ranks, they cannot however bring their hydration levels up to what it should be in that fairly short time. This leads to the fluid that should be around the brain being far less than it should, this is the real 'headguard' your brain needs but is often lacking in combat sports and horse racing. The outcome of course is that blows to the head are far worse than they should be. Jockeys of course do come off a lot, head injuries aren't always the result, a jockey this week here is now paralysed from the waist down after his horse fell, his back was broken but of course the dehydration question comes up again, our bodies have many fluids designed to help protect us including in the spine.
I would not want to spar without a mouthpiece. I heard horror storries of people getting uppercutted and they bite off their tongues.
Try sparring with your tongue on the roof of your mouth.
Many sports are now aware of the dangerous effects of concussion and the need to do everything to avoid them. One of the things England rugby are concerned about and this I think carries over into martial arts is the reporting of concussions from training and elsewhere.
"To prevent recurrent concussions and the rare but potential risk of prolonged or severe injury, coaches, teachers and parents must encourage players to report concussions that occur during games and training sessions, and to report concussions that occur out of rugby. It is also essential that school and club coaches communicate between themselves if a player is concussed, and involve parents in these discussions." A KO in a fight may cause little damage but the accumulated damage from training may be the thing that tips it from being a minor concussion to a massive brain injury. Most people who turn up to fight in MMA fights ( again not the top rank though I'm not actually so sure) say they are fine, they don't ever mention a previous head blow, concussion or even a KO because they know they won't pass the medical. Often the medical is conducted by a paramedic or even a first aider with little knowledge of what to look for if there are indeed any signs to see. We need to educate people on the dangers of blows to the head, if a child bumps it's head at school/home etc which they often do we shouldn't then allow then to carry on in a martial arts lesson where the chance is they could get hit again. You might think a parent bringing a child in like that is unlikely you need to remember for many parents martial arts is babysitting! I know of children being brought in with S&D, chickenpox and a broken arm.
This is from an article on injury prevention in Rugby but
I think it applies equally to martial arts.
‘The risk of injury will never be completely absent in rugby union but our understanding and perception of risk
needs to be carefully balanced against the recognised positive health consequences of playing rugby union.’ Simon Kemp, RFU
From here.
http://www.bath.ac.uk/health/documents/basem/injury-prevention-in-rugby.pdf