Is it common Practice
 

To require a Credit Check as part of the hiring process?

No.

Usually a basic credit score is part of a background check, and many employers are doing that now. Many consider a person with a bad credit score to be a risk, unfortunately many people today have bad credit due to not having a job-

it was a scam. they wanted ME to run it and I'm not interested in doing that..

Depends of the position in the company I work for. Some insurance companys in states that allow it will use your credit score as a factor in your auto or home owners insurance

Around here it is very common for big companies. It is considered an indicator of "reputation". Same reason insurance companies run them.

yep, it is common for large companies.

My last two employers ran a credit check on me. It was a way to prove my level of responsibility before they finalized a offer letter for me. Both offers included major moves from one side of the country to another, and the company's expense. From OH to UT in 2008, and from UT to PA in 2010.

It is where I work.

A poor credit score is a handicap that costs the individual similar to obesity, smoking, alcoholism, illegal drug use, criminal record, in that it may not be fair to assess a person by it, but it is the 600 pound Gorilla in the room if checked.

One employer noted that he didn't want people in his employ that invariably had to spend time preoccupied with activities involving juggling debt on the telephone, etc. during time they should be working for him. He also mentioned that bill collectors commonly call the debtor's workplace attempting to collect delinquent monies.

Could anyone blame an employer for wanting to avoid these unproductive, time wasting activities in his workplace, and if so, why?

I believe some states (IL ??) have made them illegal as part of the hiring process.

I would agree with them if you are doing financial transations, handling large amount of cash etc.
Otherwise I think they are a poor indicator of a person.

Well, apartment complexes are starting to run them. The lower the score the less the person can handle money and the more likely they are to be trying to scam something.

Why do you think so? IF I am constantly behind on my payments, wouldn't I be more easily tempted to take a quick shortcut to better my situation? Say I am a soldier in Iraq or Afghanistan. I am worried about the bills I left behind. Suddenly, Al Qaeda comes along and says "Hey. If you give me this one little piece of information, nobody gets harmed and I give you $20K to deal with whatever you want.". If I am hocked to my eyeballs, I will be more easily tempted. Or how about this. Wifey will be more easily tempted to take her prescription pad, make a few bucks by writing unnecessary scripts to druggies and take care of some debt.

I dont mind if the COMPANY pulls them. Them Directing ME to pull it through a non reputable site is why I asked.

I think somewhere in 2000 I was asked to pull my own personal review from my previous company. What non-reputable site are you referring to? There are the Big 3, Transunion, Experian and Equifax but there are some other smaller companies. Just as when I was doing Payday Loans, we got a report thru Teletrack. They cater to different scenarios. I don't care as much about your 30 year mortgage. I am more concerned about your landlord disputes or evictions or whether you have many other payday loan inquiries.