My guess is that you get the most benefit out of a certification if you take it as a personal feedback regarding your skills.
Relying on a certification to be a replacement for individual education and experience is likely to be counterproductive.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
I know project manager with PMP and MBA who performed poorly as a project manager in an IT project; has no respect for programmers and developers, unstable emotional outbursts at fellow team members, very poor time management and quality control, had no knowledge of the methodologies and processes in an IT project.
BEA 8.1 Certified Administrator, IBM Certified Solution Developer For XML 1.1 and Related Technologies, SCJP, SCWCD, SCBCD, SCDJWS, SCJD, SCEA,
Oracle Certified Master Java EE 5 Enterprise Architect
This is true for all certifications. You can have the good without certifications and the bad with them.
The Professional advantage is that most likely someone with the certification will find their resume higher up on the list than someone without. I'm not saying I would not consider someone without the sert, but many places use it as a way to weed out candidates.
In my experience it helps in a few ways. One it shows initiative on the part of the person with the certification. Continuing education should be an important part of every career. Second it helps to determine gaps in your experience and education. There are many areas of PMP which many PMs never work with directly, but should be aware of.
The PMI certification not only requires verifiable experience but also Continuing education credits, which helps to raise the bar a little.
There are two categories of people who can pursue PMP certification. The first category is for those who have college degrees. People in this category must have 4,500 hours of continuous, non-overlapping project management experience for 36 consecutive months within the past five years. The second category includes those project managers who have not attended college. People in this category must have 7,500 hours of continuous, non-overlapping project management experience for 60 months over an eight-year period. Both categories must also prove that they have participated in 35 hours of project management training within the past ten years.
Project Managers who meet either category must file an eligibility application with PMI. Once PMI reviews an application and determines if a candidate is eligible, they release an eligibility letter. A candidate then receives the eligibility letter to take the PMP certification exam.
The other responses do a good job of summarizing a lot of advantages of the PMP certification.
But I want to point out one really important thing: understanding the material in the PMBOK(r) Guide and on the PMP exam can actually make you a better project manager. If you take the time to understand things like how to manage your project's scope, cost and schedule, how to improve the quality of your project's deliverables, techniques for managing people, etc., and if you apply them to your projects, then you'll definitely see an improvement in your projects' results.
Now, that doesn't mean that a project manager with a PMP certification is automatically better than one who doesn't have one. And there are many very, very good project managers (and programmers who understand how to run a project well!) who are very good at making sure projects come out well. But it shouldn't be too surprising that a lot of the tools and techniques that they use to make their projects come out well are things that you'll see on the PMP exam.
Author of Head First Agile, Learning Agile, Beautiful Teams, Head First C#, Head First PMP, and Applied Software Project Management (O'Reilly)