The answer to this probaby depends on the image that pops into your head when you hear the word "assassin," which in turn probably depends (for American readers) on whether you're old enough to remember the JFK assassination or the attempt on Ronald Reagan's life by John Hinckley. It turns out that this question has been asked for over 150 years. One of the earliest answers was called the M'Naghten rule (pronounced--and sometimes spelled--"McNaughton").
The M'Naghten rule resulted from the attempted assassination of Robert Peel by Daniel M'Naghten. His case was decided by a specific series of criteria, the most important of which was whether or not the individual knew that what he was doing was wrong. This rule was the primary legal doctrine for the insanity defense in the Anglophone world until at least 1953, when it was judged to be obsolete.
I became interested in this history when reading Destiny of the Republic, about the assassination of James Garfield. I won't go into details about his case, but they are interesting in their own right and the book is highly recommended. Allow me to share the author's description of the rule's impact, which reminded contemporaries of an earlier attempt on Queen Victoria's life by Edward Oxford:
"We have seen the trials of Oxford and MacNaughtan conducted by the ablest lawyers of the day," Queen Victoria had written in disgust to Peel after the M'Naghten ruling, "and they they allow and advise the Jury to pronounce the verdict of Not Guilty on account of Insanity,--whilst everybody is morally convinced that both malefactors were perfectly conscious and aware of what they did!" Before her eventual death in 1901, at the age of eighty-one, Queen Victoria would survive several more assassination attempts. Her husband, who had lived to witness four of them, was convinced that the would-be assassins had been encouraged by Oxford's acquittal.
This last part strikes me as interesting because of its irony: supposedly insane individuals were thought to be more likely to attempt assassinations when the likelihood of punishment was reduced.*
What does this mean for contemporary political science? Over the past 35 years, and particularly in the last decade and a half, the question of whether assassins, terrorists, insurgents and the like are rational has been a critical but mostly unproven assumption in empirical research on political violence. If it turns out that assassins are more likely to strike in countries where the M'Naugton rule was in effect, this would suggest (but obviously not prove) that assassins respond to changing costs and benefits of their actions.
Further reading: Experts Disagree on Psychological State of Norwegian Killer (via @intelwire)
* Note: I am not in any way advocating for a lack of legal sympathy for mental conditions. This post is meant to demonstrate the possible rationality of a supposedly irrational act.