Although there are important variations from state to state, typically you are responsible for the personal injury of anyone who comes onto your property, regardless of the reason why that person was on your property. Traditionally, there was a distinction made based upon the reason why a person was on your property - was the person there as an invited guest, was s/he there trying to sell you something, or was the person a trespasser. The traditional degree of duty owed depended upon the person's status or reason why s/he was on your property - the highest degree of care was to invited guests while little or no duty of care was owed to a trespasser.
Traditional distinctions based upon a person's status on your property have given way to a general obligation to all persons entering upon your property. Under this trend, you may be responsible for personal injuries sustained by anyone who is on your property, regardless of status. Thus, some states even will hold you responsible for personal injuries suffered by trespassers who come on your property. It could be possible in some states for you to be held responsible for the personal injury suffered by a burglar who comes on your property.
Further, it should be noted that "spring guns" and other forms of "traps" set up on your property are highly discouraged at law. For example, if you set a trap to catch a burglar entering your back yard, or worse, you set up a gun that is spring loaded to go off if a burglar enters your home, you may be held responsible for all damages suffered, even if the injured party came onto your property to steal from you. The theory of law here is that there may be instances where a third party innocently walks into the trap - a police officer investigating a crime or a fireman coming onto your property to put out a fire - and since innocent third parties should not harmed for trying to help you, the use of spring guns and traps is discouraged by making the person who set up the trap responsible for any harm done.
Many towns and cities have local ordinances which make the adjacent property owner responsible for the care and maintenance of public sidewalks. Under such ordinances, if there is a sidewalk next to your property, you must keep the side clear (such as removing garbage, ice and snow) and in good repair (you must fix cracks and holes in the sidewalk). If you fail to properly maintain the sidewalk, you can be held responsible for the damages suffered by a person who is injured on the sidewalk next to your property.