This happens in the workplace with co-workers and with clients and vendors. It is nice to say oh, you fire those people, but the reality is many times you are not in a position to do that. Many times the person may work in another group, division, company etc and you have to deal with them.
Overall, the response is situational. If it is a supervisor or executive that is acting this way and they have been there a while and are known to be abrasive, guess what? That person isn't going anywhere because management is well aware of their behavior and are tolerating it for some reason. In those cases, you can only control you and your decisions. Same thing goes for that one guy in the corner that no one can touch but who is abrasive as hell. If he's been there for a while and management is tolerating it, you can't do anything about it (at least not quickly). All the complaints and HR filings in the world won't help you if the company has made a decision to keep that person around. In fact, it will work against you as you will be seen as a liability, so best answer is to control yourself, and make your decision about what to do.
As for dealing with those people. If I can't change the situation and I have to work with this person then I will generally ignore the insults, moronic statements and stupidity and just answer their real points calmly and without getting excited. Doing it with a smile usually is fun because you have full control over your emotions and responses while others just flip out and get pissed.
Also, where I can't directly influence the other persons attitude or employment. I will instead start pushing them up, building them up, putting them so high on a pedestal and giving them credit for everything to anyone in a position of authority who will listen. It is simple, those on the highest perch fall the hardest. This is a bit underhanded and devious, but ironically it works quite well, especially in enterprises where sometimes these type of people are accepted by their supervisor but unnoticed by say the next level of management. If you build them up they will get exposed to higher levels and they will fall, assuming the company isn't just shitty all around.