Who is a stakeholder? Simply anyone with a stake in the project either direct or indirect.

PMBOK says that stakeholders for a project are persons or organizations  –

who are actively involved;
whose interests may be positively or negatively affected by the performance or completion of it.

Stakeholder analysis is a process of systematically gathering and analyzing qualitative information to determine whose interests should be taken into account when developing and/or implementing a policy or program.

Remember that more complex your project is, more attention you need to pay in managing stakeholders. You can do all the right things for a project, but mismanaging a stakeholder who has power, influence and interest can cause failure of the project.

Mitchell, Agle and Wood (1997-99) have come up with stakeholder analysis model, that can help a project manager in early phase of planning process to identify stakeholder and classify according to three major attributes –

Power – to influence the organization or project deliverables (coercive, financial or material, brand or image);
Legitimacy – of the relationship & actions in terms of desirability, properness or appropriateness;
Urgency – of the requirements in terms of criticality & time sensitivity for the stakeholder.

Based on the combination of these attributes, priority is assigned to the stakeholder.

Level 3
(High Priority)

7 – Definitive
Power, Legitimacy & Urgency

Level 2
(Medium Priority)

4 – Dominant
Power & Legitimacy

5 – Dangerous
Power & Urgency

6 – Dependent
Legitimacy & Urgency

Level 1
(Low Priority)

1 – Dormant
Power

2 – Discretionary
Legitimacy

3 – Demanding
Urgency

Keep in mind that  –

These three attributes can be gained or lost during the time period of the project, so pay attention when it happens.
Level 1 (Low Priority) stakeholders can increase their salience by coalition building, politics, or media influence.
Power alone is insufficient to classify a stakeholder high priority; but some times it does, for example – CEO’s favorite project.
Stakeholder analysis requires careful planning, standard guidelines for selection of stakeholders, resourceful team members who have background information, and standard set of questions that feed into the worksheet.