'I was discharged for no reason from an employer as an at-will employee"
I promise you, there was a reason. You may not know what the reason was; it may not have been a good reason. But NO employer fires someone for no reason, if only because it's not cost-effective.
"I was discharged for no reason from an employer as an at-will employee. When a prospective employer asks my former employer why I was discharged, what can the former employer say"
Anything that is true or represents your former employer's honest opinion. A negative reference is not illegal - only an UNTRUE reference is. "I didn't think Jetskijo was an effective manager" is an opinion; he is entitled to say it and you would have no legal recourse. "Jetskijo was fired for stealing" is untrue (unless you WERE fired for stealing) and in that case you probably WOULD have recourse.
"they gave me no reason for the discharge I have collected unemployment"
The two have nothing to do with one another. Whether you do or do not receive unemployment has nothing to do with your references.
Is there anything I can do to find out what they have been saying about me?
Yes, but with all due respect to seniorjudge, not the way he suggests. As an employer, there is no way in he** I would tell you what your employer said about you - if I did, no employer would ever give me information about a prospective employee again. In fact, in some states I would be prohibited by law from telling you.
However, there are services you can hire to check references for you. Or you can ask a trusted friend to call posing as a prospective employer.
The current job market is extremely tight, and people are having a lot more trouble finding jobs than they're used to. The fact that you are having trouble finding a job does NOT have to mean that there's anything wrong with your references.
Here's a rule of thumb to go by: if you are sending out applications and not hearing back to come in for interviews, then it's almost a guarantee that your former employer has nothing to do with it. Employers do NOT call for references before deciding who to have come in.
If, on the other hand, you are getting called for interviews and being told that you've made the final cut, but then are not being offered the job, then it MAY have to do with your references. Not definitely; I generally call for references on at least my top three candidates, which means that two of them are not going to get the job, and references are only one factor in making the decision (and not even the most important one, usually). But in that case, it's POSSIBLE.
Again, unless he is out and out lying about you, a negative reference is not illegal.