What is the most widely distributed crypto currency? I've been doing research to find a crypto-currency that is "fairly" distributed among the population. Being "fair" is quite subjective. We can all agree that 10 people that control a coin is not fair, but what about 100? or 1000? or 10,000?

So the question is, which crypo currency or currencies have the most distribution? And the other question is distribution the same as adoption?
As you noted, a lot of this depends on how you define your terms. In an Objectivist sense, all currencies are equally fair. :)

If we look at fairness in terms of information disparity, we can see some clear winners and losers. Information disparity is important because if insiders know that their coin is technically sound before the general public does, they can snap up coins while they're cheap.


SolidCoin had 50% of its mining controlled by special accounts that were handed out to secret parties in a secret process. (Or possibly they weren't handed out at all. There's some disagreement on that point.)  
Litecoin published its source code prior to it's launch, and allowed people to mine on a test network. At launch, its code was well-understood.


If we define fairness in terms of "one person, one coin:"


AuroraCoin is a clear winner. They issued an equal amount of coins to all icelanders. They actually verified that the people claiming coins were distinct people, and not scammers.
One of the heavily premined altcoins (there's plenty of 'em to choose from) is a clear loser.


You also ask about which coin has the most distribution, which is a different question from which one is distributed the most fairly. In terms of active users, Bitcoin probably still has the most users. (Dogecoin is catching up, though.) 

In terms of inactive users, AuroraCoin theoretically has 300,000 owners. (Of course, by that measure, you could increase adoption of your *coin of choice by putting money into private keys and emailing them to random people on the Internet.)