Severance Agreement. Most employees are "at will" - they can be terminated or leave at any time. Severance can be offered to terminated workers in exchange for waiver of the right to sue. The contract specifies the termination terms and is usually provided in event of retirement or lay-off. Circumstances vary, but they are sometimes given to fired or resigning staffers too. 

Severance agreements aren't typically arranged until dismissal or resignation is on the table, and are often specific to the situation, so require legal counsel. Consider including:

Financial terms
Continuation of benefits
Unemployment compensation rights
Any waived claims
Confidentiality
Non-disparagement
Non-competition
Trade secrets
References and recommendations
Applicable laws
Violation consequences
General release 

Non-compete Agreement. These agreements state that employees who are leaving agree not to enter a similar profession or work with a direct competitor within a certain period of time and geographic area after employment is terminated. These agreements are tricky and require legal expertise - courts are often hesitant to enforce them if they present a hardship to the ex-employee, so the former employer must prove the worker took action in violation of the agreement and that the agreement is reasonable.

The strongest non-compete agreements have small geographic scope, short time periods, and recognize the position the ex-employee may not hold. They should also include or be addended to non-disclosure agreements.

Non-disclosure Agreement. Also known as a confidentiality agreement, these protect information the company deems as crucial to their operation - trade secrets, inventions, processes, knowledge, or work in progress. These are often some of the most important documents an employer should keep on file to protect itself; as with a non-compete agreement, these are often signed upon hire but absolutely must be obtained upon dismissal. The concern in waiting to get them is if the employee refuses to sign or is let go in a fashion that doesn't allow for more agreement signing - usually an indication of bad blood that would make this type of agreement necessary in the first place.

An attorney can advise on what other agreements may be necessary for your particular business and situation, but severance, non-compete, and non-disclosure agreements are three of the most important. The last two are used with nearly every employee upon hire.