What methods and/or tools have you found most helpful in stakeholder analysis?

The stakeholders management needs : - Identify the stakeholders for your tasks and their importance / influence - Good communication skill with them and what do you want from them - Create a stakeholder planning to specify the priority and the benefits that you'll earn from each stakeholders under the partial tasks of the project.
(you could download several stakeholers planning templates on the internet for free)

Best methods are to, List down all the stakeholders list Identify key stakeholders for relevant projects Add them in top left corner of the project charter, so that it can be easily visible Schedule stakeholder communication call on timely basis, Conduct brainstorming session with them

Stakeholder analysis is done through analysing the organisation, knowing formal structure, and more importantly, the informal structures and understanding the culture.
The analysis usually takes the form of interview questionairre(s) that targets functional heads of organisation, who may have limited knowledge about the informal power structures, and have the least knowledge and understanding about middle managers and employees groups and clusters.
The best way is to be part of the organisation to perform this exercise, but if not, interviews need to be targeted to middle managers, who are directly impacted by the project you are starting, in addition to project customers and suppliers (may be within the internal organisation, great! may be external, a bit harder), and of course decision makers for your project.

The stakeholder map is excellant practice.
Divide stakeholders into4 categories A.B.C.D and then map them according to their interest in organisation and power they hold...
by doing so u can get direcrtions to achieve objectives of every single shareholder.

Tamer, Mohammad Javed, Akbar and Arif has already explained the tools &technique for stockholder

1-       Expert Judgment

2-       Meetings

3-      Communication

4-      Interpersonal Skills

5-      Management skills

For more details you can download a presentation from http://www.pmiglc.org/PD/Uploads/PMIGreatLakesChapter_Dec2011Forum_GMoore.pdf 

Put together a Communication Strategy, Organogram and RASCI to indicate roles within the Project.
I also put in a contact list that is quick at hand when it comes to contacting stakeholders.
Usually on the Organogram An escalation chart is also very useful.

Engaging the right people in the right way can make a big difference to any project success - First step in Stakeholder Analysis is to identify who your stakeholders - Second is to work out their power, influence and interest - The final step is to develop a good understanding of the most important stakeholders so that you know how they are likely to respond, and so that you can work out how to win and optimize their support.
You can summarize the understanding, so that you can easily see if the stakeholders are expected to be blockers or critics.
A good way of doing this is by color coding: showing advocates and supporters in green, blockers and critics in red, and others who are neutral in orange.

in my opinion the stakeholder analysis is somehow sophisticated issue to be explained in a short comment.
i hardly recommend to study the book "^ Freeman, R.
Edward (1984).
Strategic Management: A stakeholder approach.
Boston: Pitman.
ISBN0-273-01913-9." but in brief you need to identify major stockholders in your business.
how is their relationship with company how do they affect the company in present and how will be in future .