My ten year old boy is starting to get into it. Should I let him? Should I make him wear a helmet?
Anything can be dangerous w/o proper training.
A big yes on the helmet (and elbow and knee pads, too).
Don’t let him learn the hard way that he can’t do all the cool Tony Hawk stuff right off the bat.
Absolutely make him wear a helmet. I have worked with people who have sustained some form of castastrophic injury most of my professional life and so many of them are preventable. Some *easy * prevention rules to live by:
Always dive feet first first time. Many spinal cord injuries occur in the ole’ swimming hole or even in pools and shallow waves at the shore because divers have either misjudged depth or were unaware of an object in the water.
Always wear helmets in sports and activities which could result in your head hitting the pavement…don’t even wonder if you should. Motorcycling, bicyling, roller blades, skateboards, scooters, horses…all of them.
Always have a designated driver.
As a parent I have always let my daughter do the things she loved. My only rule has been that she do it safely. When she started riding horses her instructor was a safety fanatic. You didn’t move on to bigger and better things until you had the emergency dismount mastered. It was still hard (in my field of work) to watch her fall off horses and even get thrown off on missed jumps but I knew that she was as safe as I could make her.
So, you will have to decide what you will let your son do…no one can do that but you. Whatever you decide make sure he knows that safety is priority. 
My smartass reply would be that practicing jumps where other people have to listen to it, day after day for hours on end, can result in the skateboard accidentally becoming lodged in his lower intestinal tract.
Seriously though, helmet, knee pads and elbow pads are an absolute must, even if he’s not doing stunts.
I skated for years, and usually wore a helmet, knee pads and wrist guards. IMO, wrist guards are much more important than elbow pads, because when you fall forward, the plastic piece on the pads takes the impact safely. I don’t think I ever fell on my elbows. The key to falling in skateboarding is to slide out of it on your knees. You can fall from astonishingly high places and slide out of it safely on your knees or knees and hands (hence the importance of wrist guards). I skated for years and never got more than bruises until…
At age 30 I started skating again after having not skated for about 10 years. The second day I broke my elbow. ( And not in a way that elbow pads would have prevented. Basically, instead of falling foreward, I fell backwards on a ramp and instinctively put my hand out to catch my fall. The impact dislocated and fractured my elbow. It would have done so even with elbow pads on)
Yes, absolutely. (I spent some time working at a state hospital with a whole building of people incapicated by tramatic brain injury. The very young ones were especially tragic.)
One way to get him to actually use the helmet & pads you buy is to stress the style and coolness of them. Look at pictures in skateboard magazines with him, and ask him which helmet types are “in style” right now. Ask which type his favorite skater wears. When you go to buy them, take him to someplace that has dozens of them on display, and in lots of different colors. Spend time discussing with him what colors will look best on him, and which ones are ‘in’ right now. Remember, “Safety” won’t make kids wear them, but “style” will.
[Of course, you will end up paying for outrageously over-priced, designer helmet & pads, compared to equally effective ones at Target, etc. And you might even have to go back and buy new ones next season, when styles change. But so what? He’s your kid; is his head worth it?]
My son recently dislocated his shoulder from falling off his skateboard. He “Mel Gibsoned” it back into place, but he’s horribly bruised and should have sought medical attention. I’ll bet there’s more damage than he’ll ever know.