Hasn't the whole US adopted "at will" employment? Basically, you can quit for any reason, and they can terminate you for any reason. No employment agreement violation required.
Yes, though there are some differences between being fired for cause and merely having your employment relationship ended; for example, you can't collect unemployment benefits if you're fired for (a legitimate) cause. On the other hand, larger companies tend to make it a practice never to fire anyone for cause except in the most egregious circumstances, because they don't want to bother justifying it.
To clarify, though, the list of legitimate clauses is pretty small, mostly "for cause" means they're firing you because you did something illegal in the course of doing your job. A firing isn't "for cause" because the employee (e.g.) showed up for work late too many times.
