Do you believe it's okay to fire a customer?

I absolutely believe that it is okay to fire a client.  I have had to do it, although only a couple of times in the 15 years I have been in business.
There is no doubt that you are going to have difficult clients once in a while and, as a business owner, I feel that you need to know how to work with all personality types.
However, I also believe that if a client is getting to where you can never satisfy them, complaining all the time, and getting to where you are putting more time and energy into trying to satisfy them then what you are getting paid for, it is time to politely and professionally tell them the business relationship you have is no longer working.
And you should NEVER, in my opinion, put up with a client intentionally being disrespectful and/or demeaning in any way.
You might lose a client, but you will gain your own self respect as well as the respect of others.

I just had to do that, not too long ago. He was from another country and wanted to pay me for editing in HIS currency, not US Dollars. That would have been one-quarter the pay for the same work. I explained that I get paid in US Dollars, seeing as this is the USA, but he didn't want to pay me the US cost. I had to tell him that I wished him well, but I wouldn't be able to work for him, as it wouldn't be financially worth my time. He wasn't happy and sent me some pretty nasty messages, but he got over it.

Of course it’s okay. Sometimes it’s necessary for your well being. It’s okay to protect yourself. Having said all that, be careful how you do this. Depending on your type of business, you can just walk away from them and not let them know that they’ve been fired. I’ve done that a few times. But be careful about burning bridges.

Listening to a keynote speech the CEO of a marketing firm (35 employees) said "I don't work with 'a**holes, it's not worth it." Like some of the other commenters mentioned, be graceful, act with respect, and let them go.

Actually I do.  Being a small business, the time and resources I devote to a client is “ all in”, and in the nature of our business (Renovations) it’s super important to be able to get a good reference or testimonial for the next client. I had one who would refuse to go online and comment, or fill out a comment card.... and that’s important to me since we did beautiful work and we needed to get those testimonies happening.  I did a lot of work there over several homes, and she always told me she was happy, paid her bill.   But I couldn’t get a referral I could post online so I had to divert my attention to clients who would so I could build my business. After a year of new clients I had several real testimonials and suddenly things took off.   

I have no ‘problem’ with that lady,  ( she was actually really wonderful) but it’s just that it was holding my business back considering all the resources it was talking to do her work.   I needed those proper testimonials for future business. 

Yes and you should when necessary. 

Fire them deport them! I worked at a resort and the manger called security on a guest late at night, he in convinced other guest with loud music and yelling.

The next day, he started with me about telling his kids to stay away from some deer’s, i reported and that's when i found out he has been a problem.

They wanted to make the gust happy, but they were making even more guest unhappy.

So, at what point does a rude guest become more valuable then several other paying guests?

Most definitely. Customers who are never satisfied, who are full of complaints are not worth our time and certainly don't deserve our beautiful products.  "We think everyone will be happier if you find a different supplier. We wish you well in your future endeavours."    

Totally, if customer is not willing to do his part or is over the top with demands that does not reflect your brand promises YES! There are many ways to do that tho.