What is most valuable?
When using Selenium WebDriver you will find that most valuable feature is integration with other technologies and frameworks.
Selenium can test almost any kind of web application and it supports many types of technologies. You can write scripts in various programming languages (Java, C#, Ruby, Python...).
Another important feature is scalable remote execution platform, you can execute your tests in parallel on great number of different machines using Selenium grid.
How has it helped my organization?
If used in right way (you can build your own test automation framework) it provides great test automation coverage and boosts time spent on writing automated test scripts. It can cope with almost any commercial tool in test automation area.
What needs improvement?
It would be nice to see more frequent releases and more bug fixes. Selenium has good support, but sometimes it seems that they mark some issues to easily with "won't fix" label.
Internet Explorer webdriver has some issues and should have better support.
For how long have I used the solution?
I've been using it for one and half year, and intensely for the last eight months.
What do I think about the stability of the solution?
I encountered some smaller stability issues, but most of the time it can be solved quickly. There are also some minor issues with parallel test executions but there are workarounds for this specific cases so it can be avoided.
How are customer service and technical support?
Support is pretty good, I would rate it 7/10.
Which solution did I use previously and why did I switch?
I used a few commercial solutions in my career and Selenium offered me (almost) everything that this products did, in some cases even more. I chose it because it's open source, easy to integrate with other technologies/tools and offers everything that automation testing team needs.
How was the initial setup?
Initial setup is complex just as any other development project setup is. Selenium has no installation files, it's just a bunch of libs which you need to import in your favorite IDE and set it up. It really depends on your experience, but no, it's not that complex.
What other advice do I have?
It's an open source product, (probably) the most popular one in a whole software test automation industry. Although it's free and open source it has good support and great integration with different technologies.
If you have a good QA team with engineers which have strong technical background and experience in software development I would definitely recommend you Selenium WebDriver. It offers everything you need, you can make your own framework and architecture, based on your business and technical needs.
If you have non-technical QA team and you want test automation - Selenium WebDriver is not the right solution, you should invest in some commercial products which are easier to use and don't demand that level of technical skills from your team.