While it's a right, it is also a risk to protest. Injuries, arrests, and death can happen at *any* protest (and the very similar but different toned rallies, sit-ins, and marches to boot). People should never forget that when they go as far as to publicly display their opinion that they can get hurt and even die for standing up for those opinions. Very few protests end "peacefully."
Since protests are by nature emotionally charged, one can not predict how those around you (this includes both protestors and police) will act or react. There are alot of *young* people living today who don't remember or even know the gravity of the violent, bloody and tumultuous 50's and 60's (civil rights and viet nam protests and so on). From the current news coverage, it really seems many out there believe things can't go wrong at a protest, that because it's a right, they have an upper hand. No one seems to remember children and adults alike were beaten and attacked by dogs and hosed down during the civil rights protests.
Yes, protesting is a right, and as most protestors are adults it is usually an informed decision on their part to be there regardless of the end result. However, things need to be kept in perspective. So, no, I wouldn't bring children. If you've ever seen a protest go wrong or turn riot, you wouldn't dream of bringing your children to a protest. Under most circumstances, they aren't choosing willingly to be there. They're there because you brought them. In the case of the 60's race riots it was often circumstance.
If you're speaking about the Occupy protests, most kids probably don't even understand the depth of what is being protested. Most parrot the beliefs of their parents, not speak out for what they have come to truly believe and understand. Most probably don't understand the risk they're facing and that they could get hurt, die or witness their parents getting hurt, arrested or dying. They merely become unfortunate casualties when it goes bad...as they are only there for the parent...not the cause.