My first character just kind of did everything the game had to offer. Main questline, side quests, Daedric quests, TG, DB, DG - good or bad, just anything I came across. She was kind of my 'trying things out' character, so I didn't really play by any moral compass.
The one exception was Boethiah's Calling. There's just something I felt uncomfortable with about sacrificing a comrade that trusted you and had your back. It was the one 'bad' quest I could never do, no matter which character I played. I couldn't even do that to a hired mercenary.
My dominant character now is a Dark Brotherhood assassin. Being a child of the Night Mother, she kills indiscriminately and without question, and is only concerned with carrying out her duties. I have mixed feelings about the morality of DB that I don't really know how to describe, and I'll just leave it at that because I feel like I'd write a bunch of stuff then get confused if I were to articulate everything I feel about them. Let's just call it 'grey to black', and definitely lawless.
Then I have a hunter character who's just kind of.. your regular hunter. Doesn't kill people unless provoked or threatened. I'd say she's lawful/white - not much to her, just getting by with her animal pelts and meat.
And finally, lately, I've decided to try and replicate the 'default' Dragonborn, like the box-art Nord guy. Haven't done too much with him yet, but I imagine he'd be a lawful, hero-type character.