Frequent regicide in pre-modern kingdoms and empires is usually a good marker for revealing the political instability of said kingdom or empire, where succession crises following a ruler's death occur far too often along with assassinations by malcontents. There are many kingdoms and empires that experienced a shockingly numerous amount of such coups ending in execution or just plain old assassination. Which pre-modern state takes the cake, so to speak, in that category? We can also include kings and emperors who were killed in battle or captured by their foreign enemies and executed afterwards.
In the modern Anglophone world, the examples of the English kings Edmund I, Harold Godwinson, William I, Richard I, Edward II, Richard II, Henry VI, Edward V, Richard III, and Charles I and their regicides (i.e. not a natural death) are well known to historians and history buffs. However, this rate seems slightly paltry compared to that of some other countries in the past, even if we were to include George V (died from medicated drug overdose). The vast majority of English monarchs (and then British monarchs following the 1707 Act of Union) obviously died by natural causes.
I'd say prime candidates for consideration, with rates perhaps approaching nearly half of those who claimed the throne over any given span of time, would be the following:
* Hittite Empire - a goodly amount of assassinations
* the Seleucid Empire - plenty were killed either in battle or by other means
* Jin dynasty (265-420 AD) of Imperial China and the later Five Dynasties and Ten Kingdoms period (907 - 960 AD)
* the Roman Empire - too many assassinations to count! Byzantines included. And that's before deaths in battle are to be considered.
* ancient and medieval Persia, plenty of murder and intrigue
* Grand Duchy of Moscow and then Russia, very bloody
Overall I'd say the Roman Empire wins this infamous award, but that's just a guess. I haven't bothered making a table and doing this mathematically. I was tempted to add ancient Egypt to this list, but considering how its history is so much longer, the rate of known assassinated and executed pharaohs is comparatively smaller. Certainly the percentage of pharaohs who didn't die from natural causes is somewhere below 10%. The Kingdom of Denmark also had several of its kings assassinated, but nowhere near a rate that would justify adding it to this list. Likewise, the Kingdom of France had some very shocking assassinations (Henry III and Henry IV) and of course the execution of Louis XVI of France during the French Revolution (followed by the death of his ten-year-old son Louis XVII), but that doesn't warrant adding France to the list.