In some cases, a persons well being may be endangered by somebody encroaching on or damaging their property. We obviously must encourage verbal warnings and attempts at a non-violent conclusion over violence, but at a certain point if somebody isn't listening, you need to figure out how to make them. Sometimes that requires force.
If someone is threatening your life or you feel like your life is endanger then you should have the right to use violence to protect it. Like if there's a burglar by all means get a gun and shoot him because a lot of the time even if the burglar doesn't want to hurt you he will just to get stuff to pawn.
If this is your property and someone is trying to take or damage it, you should have every right to protect it. Even if this includes a violent action to protect yourself. Imagine that someone gets hurt or killed while they are attempting to break into your property or while they are trying to steal their wallet? Self defense exists for a reason, and that person is getting an adequate punishment.
People should be able to protect their own homes. Someone breaking into someone else's home is clearly dangerous, and probably intends to use violence. Using violence in response is, as such, warranted. I don't think that simple trespassing should be punished as harshly, e.g., I think it is wrong to beat someone up simply for walking on your lawn. However, this is where common sense and a properly written law code come into play.
In this country and in most countries around the world when you are protecting your property the use of violence is deemed appropriate. Property ownership is a fundamental human right and its defense using violent means is sometimes necessary. I would suggest that such violence be used as a last resort after more peaceful methods have been tried and have failed.
The Second Amendment protects American citizens from home invasions with the right to bear arms. If an unprovoked stranger comes onto private property, then violence should absolutely be legitimized for defense. Police can't be everywhere. Self-defense is a vital part of American ideals. No one should be left defenseless by laws preventing the right to defend one's own property from attack.
My material things are not worth people's lives. Life is invaluable, fragile, replaceable. You can replace your things, but you cannot replace a person's life. If you can stop someone from taking your things without killing them, then yes by all means, do what you need. But is it really worth it to kill somebody over meaningless, worldly things? Absolutely not.
Violence is not necessary because, as the previous people mentioned, property comes in many forms. All violence leads to is even more suffering and just makes the situation worse for yourself and the person you are inflicting it on. There are many other ways to defend your property, one example is that if someone stole or tried to steal your pen, would you really apply violence? A more serious example is, if someone tried to steal your television there are many other ways of dealing with it without using violence. Many people have gone to prison from using violence to protect their property so that is another reason why you shouldn't use it.
Violence does not help any problems in the modern world. Violence resolves nothing and just leads to suffering and death in other countries for people who shouldn't be affected by something, like the amount of people that are affected by the wars in Syria and Afghanistan. Violence should never be used and instead in countries of war and violence peace talks should happen with the enemy.
Property is whatever you own. Would you use violence to defend a bar of soap? No. Also, violence doesn't resolve anything and you could kill someone accidentally. Gandhi once said, "An eye for an eye makes the whole world blind." This shows violence in a bad light. A real life example is the war in Afghanistan. The Taliban claim they are defending their property, but so many deaths have been caused due to the conflict.