Trespass to Land
The Restatement (2nd) of Torts, section 329, states:
A trespasser is a person who enters or remains upon land in the possession of another without a privilege to do so created by the possessor's consent or otherwise.
The tort of trespassing protects the interest in the exclusive possession of the land. Anyone who has an actual and exclusive possession of land can bring action for trespass as a plaintiff: therefore, you do not necessarily have to own land to bring a trespassing claim - you just need to have the legal right to exclude others. Trespassing has two elements: An actual interference with the right of exclusive possession (called the "entry element"), and intent or negligence. Notably, there is no damage requirement, though pollution and neighbor trespass cases are an exception to this rule (they require a showing of damages).
As for the intent element, technically the person must intend to be on the land that they are on. But, in keeping with the hair-splitting often found in the nooks and crannies of the law, this does not mean the person must know that they are trespassing. To illustrate this point, imagine walking along a road, out in the country, that is bordered by a large field, which you are unsure whether it is private property or public land. In a simple example, the law draws a distinction between deciding to cut across the property (trespassing), and say accidentally meandering off the road in darkness (no trespassing). But, lack of intent is not a complete bar to prosecution - negligent acts that lead to entry can be prosecuted as well. So, if instead of walking along the road at night, you were driving along at an excessive speed and accidentally left the road and entered the property, trespassing would likely be found.
Trespassing should be contrasted with nuisance, which protects the quiet enjoyment of land. The major differences between the two torts are that nuisance claims need to show both damages and that the invasion was unreasonable - elements noticeably lacking in trespassing.