Ashley has it for the most part spot on.
I'll also start with the disclaimer that I'm no lawyer, but as a semi-professional original musician I've had to do a lot of studying up on copyright law in order to better protect myself.
So, first off, to clear up a few misconceptions about U.S. Copyright Law:
* If the character itself is someone else's creation, you need a license given by the copyright holder to use the character (in most famous characters' cases, it is a company, often cold and heartless <img src="smileys/smiley2.gif" border="0" align="middle" /> ).
* Non-profit does not equal fair use. Copyright is what you'd call "as advertised". It means that only the copyright holder has permissions to control how their creation is copied, in any way, shape or form. They can issue licenses to third parties, for a fee or for free, but they still get to control who gets those licenses, with a couple exceptions.
* The exception, in the case of music, is a compulsory license. That, however, is not applicable to your case, as that deals only with covering songs, not for doing things like compilation albums, which needs a different licensing deal. You'd need to obtain a different license to use someone else's characters.
* Fair Use laws come into play when dealing with commentary and parody, or for educational use (though educational use is more meant for examples to teach classes, does not actually qualify for fan games). It has nothing to do with percentages or an infringer's economic profit. A copyright holder could sue you for dilution of brand if they'd like (I make a god awful Mario game that could give people who don't know Mario a bad impression of the plucky plumber, which would hurt future Nintendo sales), or if an infringer's product obtains the specific demand the copyright holder's product or potential products would have held (if I made a free Mario game that was better than Nintendo's $50 Mario game and people substituted Nintendo's game with mine instead, that equals lost earnings for Nintendo).
Some companies don't mind people using their sprites and characters in free fan games. Capcom is famous for unofficially supporting it. Others, like Nintendo, often turn a blind eye to it, unless it could potentially compete with their own products, in which case they almost always just send a cease and desist. There are just so many people out there, and sending a cease and desist to them all would be a waste of time. You still risk a lawsuit of course. That's their right.
I'm sorry if that's a lot to digest, but copyright law is a complicated affair that's meant to protect everyone from all sorts of scenarios.
Are you allowed to, by law? For the purposes of your fan game, not without a license from the copyright holder. You can decide for yourself whether or not you feel your use would be ethical and if the risk of you being taken to court is worth it.