I work for a small company and have been lucky enough to build a great relationship with the this company. Such a good relationship that when it came to time to sign a work contract with them, they refused to issue one and we just agreed to terms with a hand shake. I don't really know what this means by way of employment rights. If I get fired, do I have any rights? We agreed on a considerable amount of money for one year and receive full benefits.

Any advice would help.

Thank you everyone.

If there's no contract, you don't have a leg to stand on (no rights). This is indeed a great relationship, but only for the company. It's a terrible relationship for you.

If your state is an "at will" state, then either of you can terminate employment at any time for any reason.
What kind of rights do you mean? If you mean salary and benefits there isn't much you can do without a contract.