As I see it, there are 3 general categories of risk with stealth camping: Nature, crazy people, and the law. (Typically they're not all in play at the same time.)
Nature is mostly referring to dangerous animals, but it can also mean storms or perhaps even tree branches falling on your head. Checking weather.com (and moving or paying for lodging if need be) should be enough to stay safe from the weather. And common sense about where you lay down (and perhaps using a tent or some other shelter if) should keep you safe from things falling on you.
I don't want to bump into a dangerous animal. I figure against a crazy dude or a disgruntled park ranger, I at least have a chance. There's always hope to reason with a fellow human. But if a bear wants to eat me, he's probably going to.
But mathematically it's unlikely. Generally animals don't mess with humans. Even very dangerous animals like lions (as far as I understand) choose
their battles selectively, and probably don't want to mess with
you even if they see you. I don't know the odds, but doubt it's really any more significant than the chance of a gas tank exploding or your house catching on fire or something like that. Risk surrounds us constantly, and that's important to remember.
I'm cognizant of the risk any time I camp in a wilderness sort of environment, but I don't actually worry about it. You can carry some sort of spray or knife if you'd like, and of course you can tend towards more urban/suburban camping sites.
Crazy people doing you harm is another possibility, but generally an overrated one. If you told the average Joe that you sleep outside, he'd be blown away and insist it isn't safe. He imagines crazy people coming to get you in the middle of the night. But it turns out this doesn't actually happen.
Most people who want to do you harm aren't looking for you in the woods. (Even if you're in an urban or suburban environment, they're still not looking in the woods. They're roaming the streets or looking for a house to break into.) And in the off chance someone randomly stumbles into you in the woods, he most likely doesn't want to do you harm.
It's not impossible that the planets could align where somebody hurts you, but it's not very likely. Someone can hurt you in a house too. The house gives you a layer of defense, but the other side of the coin is it advertises that you (and your stuff) are in there. Seems more likely to me that a bad guy will pick your lock than he'd find you in the woods.
Sleeping outside only becomes a danger if somebody knows where you are. If somebody saw me carrying around a laptop or some other valuable and he knew where I camped, obviously that's a danger. Common sense: Don't tell people where you sleep, and don't walk to where you sleep if someone is following you.
Finally, there's the law (cops, park rangers, or maybe even private property owners). I don't recommend doing anything illegal. The law isn't always clear or easy to access, in general I think stealth camping is legal, but even still a police officer or park ranger might wonder what you're up to if he sees you.
I'll never camp anywhere that's marked as private property (or that's clearly somebody's backyard or something), and I'll always clean up after myself wherever I do camp. I try to be a hassle to nobody and follow all rules and common sense. Even if a cop would disagree with what I'm doing, he doesn't suit up in the morning to find me in the woods.
If you do get hassled by a cop, I recommend one of two extreme strategies: Be very friendly and highly cooperative (point out that you were just passing through, you made sure not to litter, etc.) --or-- refuse to talk to them entirely. A mixed bag approach where you talk to them but give them attitude is probably your worst play.
The US legal system is grossly inhumane. Make no mistake about it. Millions of innocent people are locked behind bars because they got caught with the wrong kind of vegetation in their pocket. But use what you can to your advantage: You don't have to speak to cops. In the case that they catch you camping somewhere, chances are they're just curious and it's probably worth a shot at being friendly. But if you get a bad vibe or they press you for information that you don't want to give, don't engage them. Politely tell them you'd like to exercise you'd rather not answer their questions.
I don't think the risks of stealth camping are any different than the general risks of being alive. We're always roughly as safe as the society we live in. Sleeping outside just changes the variables.