I am new to Paradox games and am leaning towards starting with Crusader Kings (the first). Does this game have the option to execute persons within one's own government or military leadership? Many of the kings throughout history cleaned house when they took the throne. It would be neat to be able to "knock off" people who annoy you within your own ranks. Thanks :)

You can assassinate people in Crusader Kings, yes. There is a percent chance that you are discovered in your attempt, but it can be done, yes.

Is the "assassination" feature for enemy kings and important people only? Or can you knock off your own people too? There shouldn't be a "chance" of knocking off your own government leaders if you are the supreme ruler.

You can attempt to assassinate anyone you want, including children. Your intrigue score will increase your chance of success.

"Send Assassin, you can get rid of an unworthy successor or an infertile wife, it will cost you gold, but if the attempt fail, it will cost you prestige and piety as well, and your reputation will take a hit. Attempts on high profile characters will be costly and the chances of success will be slimmer."

Thank you very much for the information. That answers my question. So it is "assassination" not "execution". I have played several strategy games with assassination (with risk of failure) options but have yet to find one with enough historical accuracy to include a true knock-off option, as kings throughout history did regularly (and Kim Jung Un does even in 2016). For the record, I do not approve of this in real life, obviously. I just think it was be more historically accurate to include this feature.

I didn't play CK1 much, so I don't really remember. But in CK2, you can imprison your subjects, and then have them executed or exiled, or let them rot in your darkest dungeon (where they will die of illness), or take their lands, or have them "promoted" to be the court fool, or castrate them... Some of those will only be available if the subject misbehaved (rebel, part of an assassination plot, heretic, etc...), others only if your crown autority is centralised enough, or if you're the right culture/religion. Even the king has to respect the law, after all.

And in every case, being too harsh or too arbitrary will cause anger in your vassals, which will be a problem since CK is all about personal relationships, family ties, vassals-liege, etc...
So you can be a tyrant, but it comes with a price.

Don't remember if it's there in CK1.

I played CK quite a bit some time ago (but never yet CK2), and can't recall anything alike, so I think there only assassination in CK1.