I'm (slowly) working on a game that hinges on the idea of "doing good" and "doing bad" (where "bad" is something that's detrimental or harmful to others (NPCs, the environment, anything), and "good" is the opposite of that... whatever that is). However, I'm struggling with how to represent "doing good" and "doing bad" in a game in such a way that it allows for fun game mechanics while still getting the point across of good/bad.
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I haven't really settled on specific game mechanics (i.e. is it a puzzler, or platformer, etc) because I'm unsure of how to represent doing good and doing bad, and I want the game mechanics to nicely blend with doing good and doing bad, so I'm taking a step back and thinking of various ways to do good and bad.

I think you have already answered yourself: if you define evil behaviour as being harmful to characters and to the environment, you can tell how evil the player has been by measuring the well-being of any entity you care about. Obviously, the player has to be aware of how he's doing; only attributes and events on which the game offers feedback are a fair measure of good and evil behaviour.
Examples:

• In a SimCity-like game, measure various types of pollution and citizen unhappiness. An unlucky or unskilled well-meaning player might get bad grades, but it should be an exception; there should be serious temptations to neglect people and accumulate money, or to be lazy.
  
• In a strategic or campaign-oriented wargame, war is nasty in any case, but some unnecessary bad things are a good indicator of a careless and callous play style: low troop morale, excessive casualties, civilian victims, damage to infrastructures, loss of crops, and other types of collateral damage that apply to your setting.
  
• In a driving simulation, evaluate property damage (e.g. accidents with other competitors and with random vehicles or trampled obstacles) and in some cases driving offences, endangered spectators, etc.
  

woh, back up for a second. The main problem with your brain going "what?" with good/bad is because that is not what your aiming for. Many players mistake the actions within a game as predetermined good/bad mechanics when in fact it has nothing to do with that.
First off, lets pretend your world is grey. That is, there is no good or bad at all.
A cat lay on the ground, hurt. You walk past it.
That was wrong, your world got a little darker.
Instead you decide to carry the cat home, and fix him up.
That was right, your world just got a little lighter.

I'm using colors here to explain it in simplistic terms, most game mechanics related to this are designed around wrong/right actions a player chooses. When you attempt to imagine things that are right or wrong, it becomes a lot easier.
And no, it is not the same as "good/evil" as many of you will think. Wrong/right is working off your moral compass, which is basically what you've been told is wrong/right when growing up. Good/evil is more of a generic term that explains the "world's" moral compass as such, not yours. One person can think something wrong, while another person can think that same thing right. Yet both will agree its evil.

So glance back to your previous thoughts, and think in the terms of right/wrong instead of good/evil.