If you received health insurance through the Marketplace, then yes you still need to have Form 1095-A. That is the only required health insurance form. For anything else, you just need to note whether or not you have had insurance during 2016.
If you have a 1095-B, a form titled Health Coverage, the IRS does NOT need any details from this form. You can keep any 1095-B forms you get from your health insurance company or the government agency that sponsors your plan for your records.
If you have a 1095-C, a form titled Employer-Provided Health Insurance Offer and Coverage the IRS does NOT need any details from this form. You can keep any 1095-C forms you get from your employer for your records.