Complete Agreement - Insist on a written settlement agreement addressing all relevant issues, not just a check.
General Release - If you're an executive level employee, and especially if you were employed by a closely held or family business, request a general release. This is a separate document, or provision in the settlement agreement confirming that the employer (and anyone else that might be named, e.g., individual owners) have no claims against you. You want to know that when you leave you're really done. If there is an open issue that the employer might have (e.g., a possible claim against you on one client account you serviced), that one item can be identified and excluded from the general release so that both you and your employer know what is open. There is no point in your negotiating a large dollar settlement to find that you have a claim against you for even more.
Fairness - Most employer-drafted settlement agreements are totally one sided and have you as employee release the employer without comparable provisions for you. When the tenor of your comments on the agreement your employer gives you are asking for equivalent treatment, there is a fairness to your requests that may help you obtain some concessions even when dealing at a disadvantage relative to the power and financial strength of your employer.
Covenant not to Compete - If you signed an employment agreement it probably had a covenant not to compete. Unless you're retiring, get a release from that restriction so you can work anywhere. If you have a new job that you don't think violates the covenant, have the employer acknowledge that in writing so that you won't have a problem. Even if the new job is not subject to the restriction a vindictive employer can intimidate your new employer into not hiring you. In many cases your employer may have specific concerns about an old covenant not addressing issue that are now of a concern. It's often possible to revisit and modify the covenant to accomplish additional goals that everyone wants addressed.
Reference - Get a letter of reference now so that it cannot be withheld later. The form of letter could be attached as an exhibit to the settlement agreement. That way, when you need a reference you know what you'll be getting.
COBRA - You can continue health insurance coverage until you get new coverage at your new job. Don't accept a lapse because there then may be issues with a pre-existing condition and getting new coverage. Although COBRA is governed by law, be sure to look into it as you may have special benefits from a plan at your employer, or state law may provide for greater protection. Know your rights and address them.
Assets - Clarify issues on your use of names, customers, etc. It can be easier to resolve these issues up front than have a fight later. For example, if you have written articles, or have a rolodex of names, can you use them? Who owns what? Clarify it now.
Tax Status - How are the payments you have or will receive from your employer as part of your termination being characterized? Are they payments for past services? Emotional distress that is causing you to leave? Other items? This can have a huge tax impact. Be certain that your agreement states not only the amounts you get, but what they are for, and what the tax ramifications are.
Equity - If you owned equity in your employer's business, negotiate a buyout as part of the settlement agreement. Also, if the employer is an LLC or S corporation, confirm what the distributions and tax consequences will be. Most closely held businesses are organized as S corporations or LLCs and income flows through to the owners. You don't want to have to report income on your personal tax return, without a distribution of cash to pay the tax.