Are they mostly ordinary folks like you and me who just snap? Or are they disproportionately likely to have criminal records?
I know of no truly comprehensive data on this, but here's what we learn from the intentional homicide line in Justice Department's Felony Defendants in Large Urban Counties, 2004 (a sample that is representative of the large urban counties that account for roughly half of the nation's violent crimes):
83% had a prior adult arrest (compared to likely 25% or so of the adult U.S. population).
76% had two or more prior adult arrests.
55% had five or more prior adult arrests.
65% had a prior adult conviction.
44% had a prior adult felony conviction (compared to about 7.5% of the adult U.S. population, see Christopher Uggen et al., Citizenship, Democracy, and the Civic Reintegration of Criminal Offenders, 605 Annals Am. Acad. Pol. & Soc. Sci. 281, 288 (2006)).
This does not include "arrests or convictions that occurred while the defendant was a juvenile" (I quote here from an e-mail from the author of the report). Since nearly half of all homicide offenders are 24 or under, the exclusion of juvenile arrests and convictions is thus likely to substantially undercount the actual arrest and conviction record. This also doesn't include arrests or convictions that the state effectively expunged or never logged, for instance because someone was allowed a "deferred adjudication," which is essentially probation in lieu of a conviction, so that no conviction would be entered if the probation is finished with no observed violations.
Note that these numbers have been increasing in the past decades, though I can't tell whether this is because changes in who commits crimes, changes in criminal apprehension rates, or changes in states' keeping good track of criminal histories.
(Reposted to fix a glitch that blocked submission of comments.)