that I saw once $600+? I went there for a checkup and PAID my 40 dollar co-pay. This check up was done in November of 2006, and the letter from my health insurance company said that they would not cover the cost because the claim was filed/ received of November 2007- more than a year later!

This isn't my responsibility right, I paid my copay and that doctor's office was supposed to do the rest. How do I handle the situation?

Don't worry about it...you are only responsible if you did not provide your doctor with your insurance information in a timely manner.
I am going to assume you have either an HMO or a PPO policy since you have a copay. In this case, the provider (doctor) has an agreement with the insurance co. stating that claims must be filed within a specific time period (usually 90 days).
The claim did deny for timely filing, but if you look at your claim summary that you received, it likely states that your liability is $0.
The doctor can always appeal to the insurance...and if they have a good reason as to why they waited so long to submit the claim, the insurance will likely pay anyway.

You are correct. The insurance company was not telling you that you owe the doctor, only that they are not going to pay the doctor. If you get a bill from the doctor you will need to contact the insurance company and get something in writing stating that they would have paid if the claim had been filed within timely filing limits. This prevents the doctor's office from being able to come after you for the $600. Ultimately, don't even worry about it until you get a bill from the doctor's office.