In my opinion, every process involved in project management, from the initiation phase to the closing phase is just as equally important as the other. During initiation, you are trying to turn an idea into a goal. One simple idea can be a game changer in any sector of life. Implementing the right idea is important because there would be no project without this stage. From the smallest tasks to the largest tasks, planning sets the roadmap for the project. Executing the actual work displays where things may go wrong, trial and error. Lastly, closing is important because you want to verify that everything goes right for the final delivery. Like a domino effect, if one stage goes wrong, then so does the other which is why it is important to verify that each stage is treated equally. 

Some projects are relatively straightforward and predictable. Others are highly complex and risky. Each requires a different approach when it comes to how the project should be managed. Applying the same amount of project management rigor to every project is wasteful.

Personally, I think the planning phase is the most important phase of a project.  While I agree with Meagan that all phases and processes are equally important, I also believe that without a solid planning phase, where each step has a back up plan for the back up plan, the project will not be a smooth one.  The project would most likely get delayed multiple times and end up costing more money than initially planned.  

I believe that each of the phases are important, but the planning phase may be slightly more important than the rest. This is because without very good planning, the cycle: plan > do > check > act, would not have meaning. You can only get as much effort out as what goes in. Don’t expect a quality output if the input was not thought out.

I believe the development phase is the most important. By this time most of the groundwork for the project is complete. The planning and design phases are complete, and major project deliverables are beginning. The project team begins to finalize their design documentation and begins executing. DFM and DFI (Design for Manufacturing & Inspection) begin. The team must work to get their first prototype and develop V&V plans. The development phase can be what makes or breaks the project. 

Since every project is different and ranges in sophistication and complications so there will definitely be one phase or process that will outweigh the other when comparing projects. However, it makes sense for the planning and development phase to be the most vital stage of most projects because it's the processes that set the stage for the whole project. If the foundation isn't there the project may not pan out successfully. 

I agree with the above posts that every process involved in project management is equally important, as they all play a critical role in the final outcome. However, as mentioned above I agree that the planning phase might be the most important. This is because the planning phase is foundational to the success of the entire project. A good planning phase will set the team up for success and the ability to deliver on time. Aside from the planning phase, the project execution stage is extremely important because this is when the group kick starts the work. Successful execution is critical to the final outcome.