You'd have to:
-Not take the thieves guild
-Not take the side of the Stormcloaks
-Not take the Dark Brotherhood quests
-Not destroy the Dark Brotherhood (unless you want to murder someone who belongs in jail)
-Not take the side of the Empire
I don't know about the companions, but I'm pretty sure there's questionable mercenary-work there as well.
It'd definately have to be an archer, because swords can hit the wrong guy a lot easier than arrows (the irony...)
What's wrong with Mercenary work?
You get to clear out threats to the general public, and get paid for the trouble.
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What's wrong with taking money for a task to find and kill / kidnap / harm in individual who may or may not be innocent, or destroy / steal his property?
Being a mercenary implies that you do not ask questions to the quest-giver to make sure there is justice in your quest.
It implies that you are a tool, that is used by the person hiring you for good or evil.
In the end, a mercenary is a tool.
Mercenaries are not the same thing as a private investigator / adventurer / law-enforcer / knight / concerned citizen.
Mercenary taking a job:
Quest-giver:
I want you to bring me Person.
Mercenary: How much do I get for bringing you this... Person, and is he dangerous?
Quest-giver:
I give you 1000 gold, and Person will be unarmed.
Mercenary: *** Fetches Person and returns him without listening to Person's pleas ***
Quest-giver: *** Pais mercenary 1000 gold, and sends the mercenary on his way ***
Concerned citizen / Good character taking a quest:
Quest-giver:
I want you to bring me Person.
Good guy:
Why do you want him kidnapped?
Quest-giver:
He has offended the laws of my people, and must be brought to justice
Good guy:
What did he do?
Quest-giver:
He refused to marry my daughter, and must be put to death!
Good guy:
:down: Forget it. I will go warn him about you, and PLEASE draw that dagger of yours; I'll drag YOU kicking and screaming to jail where you can rot for quite some time, for attempt of murder!