Testing conducted to evaluate a system or component at or beyond the limits of its specified requirements. [IEEE]
BS 7925-1.British Computer Society Specialist Interest Group in Software Testing (BCS SIGIST)

Note I suggest Stress testing is quite distinct from Load Testing. Here the aim is to discover how the system will behave when it is pushed beyond the non-functional requirements. This situation will typically occur when the customer pushes too hard. The developing organisation may only support up to the load requirements. However they do need to know when it is likely to happen. This sort of testing is essential for safety critical software.

Indeed Stress testing is often used inform the decision about setting safe load instructions for end-users

Load testing, however sets out to confirm that the system does operate within defined parameters when set within the requirements levels.

An essential element of stress testing is to log everything. This is because a number of steps would have gone to before a failure occurs. Additionally you need to know exactly the state and environment the application was operating in at the time of the failure. Typical metrics include how many concurrent users there were or transactions trying to take place.

If a database is used, ensure transactions add, amend or delete records continously. Doing so enables checking on record locks, memory leakage or if the database is growing at too fast a rate.