Here's my followup to the post I started yesterday.
If the insanity defense were reformed (again), you'd have to decide which new legal test you'd use. A legal "test" is a written definition or standard. In general, there are two insanity tests in common use: the ALI test and various derivations of the McNaughton test. The McNaughton test states that a defendant is insane if he is unable to understand the nature or quality of the act, or---if he did understand the nature of his actions---that he didn't understand that they were wrong. In 1955 the American Law Institute (A.L.I.) wrote the Model Penal Code in an effort to make criminal laws uniform across the country. The Model Penal Code's insanity test, also called the ALI test, states that a defendant is insane if he "lacks substantial capacity to appreciate the criminality of one's conduct or to conform one's conduct to the requirements of the law". It has two parts, a cognitive standard and a volitional or behavioral standard.
Here is a link I posted last year to a state-by-state break down of insanity standards. It's a little out of date; Kansas is listed as using the McNaughton test but they have since abolished the insanity defense.
Frontline did a nice series a while ago about the insanity defense and they have a summary of the historical tests here.