I don't have any particular officers that I always execute, but I have a couple general rules. The first being that if the officer has a horrendously ugly portrait or otherwise has some annoying intangible characteristic, he gets the ax. I kill Chen Shi on VI a lot because of this. Mi Fang is generally a good bet as well because he usually looks like a goof. He's also a good candidate because of my second reason. Anyone who betrays me and defects at any point in the game I will execute when I catch up to them. No exceptions.
I also kind of like to execute Liu Bei, but I try to hold off as it also means executing Zhang Fei and Guan Yu and I'm much more fond of them. I'm kind of trigger-happy though to be honest.
I kill most rulers who don't join me because I don't like to release them and have them floating around in my territory refusing to join me for the next 10 years. Unless it's someone I like I've also been killing anyone who doesn't join me after the initial "recruit" command and then the second one after a one year imprisonment. (I play VI by far the most. III is awesome too.) In my game as Wu in 234 I've been patiently waiting trying to mostly play defense to wait for Sun Xiu to arrive and then ascend the throne, but Wei has offered me a couple irrestible opportunities. They keep attacking Jiang Ling and getting beat down so I started executing everyone just to spite them.
Back in the RTK IV days I used to execute Ma Teng all the time because in my first ever game of RTK he invaded Zi Tong and killed Yang Huai. This made me angry and I found much satisfaction in taking him down. (I completed that game with Wu Yi as my ruler instead of passing the throne to Liu Zhang. I had no idea about the story or releationships.
) I think I also had a vendetta against Cao Cao in that game, but none of that stuck.
So I guess it pretty much just depends on game situations, though I probably execute more than most here.