I can never come up with a decent character in the Morag Tong. Do they do it simply because they enjoy it? Out of reverance for Mephala? To pay the bills? Can one play a character who is generally a nice chap who just so happens to murder people indiscriminately on a regular basis? And which other factions do such characters join?
What do you think the differences between public, private and house war executions are?
Do you think members can retire? Apparently, it is unorthodox for the grandmaster to do so but this might not apply to the lower ranked members.

The only two things I can think of are reverence for Mephala, or just being a violent person. I can't see a nice person consciously seeking out the Morag Tong for employment. However, it is apparently supported by the goverment and it does target criminals, almost exclusively.

So, maybe it would be fit for a Charles Bronson vigilante type character. Maybe they could start out in the Imperial Cult or Legion then get expelled because of their reckless methods.

I could also see Telvanni coinciding with the Morag Tong. Both are pretty morbid groups of people.

This is exactly why none of my characters ever joined the Morag Tong. I could never come up with any roleplaying explanation for why they would do it.

I was blackmailed into joining.

My Argonian is a member because he's your Duke Nukem / Terminator / stuff type of a bad ass. He comes without stupid catchphrases though. And there aren't sunglasses in Morrowind. Immersion? Bah! That guy could use a pair of sunglasses after an assassination.

So, he makes a living by assassinating people. There's kinda much money moving in that business. Nothing personal, nothing special. Just another day at the office. He's going to be the Exalted Master and then waiting the current Mr. Big Shot to retire peacefully when he so wishes. (Never! I like Eno Hlaalu too much to let him go. :′()

Sometimes this Argonian murders some guys if they just annoy him too much. Call them gray writs if you will. This man is a bounty hunter. That's just what he does best. I don't know if he's generally a bad guy though. He might steal. Okay, he might murder occasionally. Just your average bounty hunter thing going on though. He's not some aggressive madman, though. A cunning Argonian, not a savage Orc.