People don’t have to intend to cause harm in order to be guilty of crime. In many instances, behaving recklessly is enough for a conviction. Two common examples where recklessness is at issue are reckless murder and involuntary manslaughter. (See Murder vs. Manslaughter: State of Mind.)
In general, someone acts recklessly by understanding that a particular harm will result from a certain action, but nevertheless taking that action. Someone in this position doesn’t intend to cause the harm in question, but disregards a substantial and unjustifiable risk of causing it.
In order to prove recklessness in a civil case, it typically suffices to show that a reasonable person would have understood the risk in question. But to establish that someone was reckless in a criminal case, the prosecution must usually establish that, regardless of what a reasonable person would have understood, the defendant actually recognized the risk. (Safeco Ins. Co. of Am. v. Burr, 551 U.S. 47 (2007).)
With the above said, some criminal courts may consider both what the defendant knew and how a reasonable person would have acted. And a jury may be free to determine that a defendant subjectively recognized a risk if it’s clear enough that a reasonable person would have done so. (State v. Keend, 140 Wash. App. 858 (2007).)
For more on this issue—that is, the distinction between negligence and recklessness—see What is criminal negligence?
Example: Jesse approaches Brandon and confronts him about a disagreement the two had while working together. Jesse punches Brandon in the jaw, breaking it. The prosecution charges Jesse with second degree assault. In the state in question, second degree assault incorporates both intent and recklessness: It requires that the defendant intentionally assault someone and thereby recklessly cause significant injury. (If the crime required that the defendant intentionally assault someone and intend to cause injury, it would be a specific intent offense.) Brandon is probably guilty of second degree assault, as the prosecution shouldn’t have trouble establishing that he knew a punch to the face would risk a serious injury like a broken jaw. (State v. Keend, supra.)