These people usually end up eliminating themselves. Try not to take them too seriously and move on.
Banning Accounts

@OP: Have you reported these excessively abusive individuals? The best method for reporting them is to fill out a Support Ticket, through Help & Support. I can assure you, from my own experience, that Chess.com does not tolerate vicious rudeness and racism as you describe. Through Support Tickets, I have been instrumental in getting a number of them banned.
I am truly sorry that you have dealt with such unpleasant people. However, in order for Chess.com to catch and ban these members, we need to do our part to help the site find them. I hope your experiences improve from here.

Hi,
I completely agree with you Reverse_Justice. I propose to create a blacklist of members that offend or insult their opponents. And this list must be notified to all members of this wonderfull site . By doing so, all members will know who are those unpleasant people, and surely will avoid them. I think this is the best way to penalize those unpleasant people.

Just a thought, but how about a feedback system similar to ebay? That way those people who are prone to insulting others will soon get adverse feedback. Tournies and chess challenges could then set criteria to prevent these people playing. It's clearly not full proof but may be worth considering. Thoughts?

You know, most of the people that get taunted or cursed during a chess game most likely have done something to deserve it. I don't think we know the whole story here, folks.

Come on John, get real. Although not a common occurrence I personally have recevied abusive chat with no reason. I think you may be a little niave to think that there aren't people out there who just enjoy being abusive. I grant you that some cases will involve retribution but many are simply arse holes acting like arse holes!

@ Mr. John:
Like I said, of my hundreds of games in chess.com I have only met 2 people who were insulting enough to really pay any note of their abuse to.
However, John, in your scenario it would seem that someone would have been guilty and nasty in the first place. Their is always an initiator in correspondence such as chess.com. Thus what I have gathered from your theory is that I am guilty?
Supposing your theory is correct, that would mean someone initiated unpleasantness. So if beating someone gives good cause to speak abusively, yes he was completely justified.
@whirlwind: I will check this out and report the individual. If he was this angry from just beating defeated, I can safely imagine he is a repeat offender. If not, then nothing will happen. Either way nothing bad will happen from it.
Is there really no way to ban horrible offensive players from chess.com?
Most people here are very nice, but sometimes(luckily in my case only 2 people) have just been very sore and viciously racist (which is funny considering they always get my race wrong just because I have the Japanese flag).
In these instances I merely responded by blocking them and telling them they are among the sorest players I have ever faced, but what about people who can more offended than myself?
These players could really mess with someone's day if they manage to come across a more sensitive or younger player.
Is there no way to implement a warning/character rating system? That way people know who to avoid if these types of people disturb them?
I'd prefer to be able to play productive players, who have the thought capacity to analyze a game with you rather than complain.
Sorry for wall of text, readers enjoy.
EDIT: I have noticed 3 of my opponents have been banned, but I noted them to be fine fellows, who conversed well and seemed to be good players.
One said he was banned for spamming he did not do. Why is spamming held at such a high priority, but blatant racism and rage tolerated?
Eliminated such ragers would vastly improve the chess.com community, spammers can be annoying, but if it is possible for someone to be banned for spamming that was proven to not have been done (and be unbanned within a matter of days upon proving it) there is something clearly wrong with that system and it should be rethought/set aside until ragers are taken care of.