The advantages of following a project management methodology are:
- You don't have to reinvent the wheel: A project management methodology provides you with a tested and proven framework and process to manage your projects. It will become much easier for you to manage projects.
- It's easier to handover projects: When you are using a PM methodology, then it becomes easier for another project manager to take over the project (because he is familiar with the whole process) in case you decide to resign from the company or if you're moved to another project.
- You will be able to learn from the community: There are two major project management methodologies, Waterfall and Agile. Both have very large followers, and a lot of these "followers", whether Watefallists or Agilists, try every day to make the methodology better. As someone who's using one of these methodologies, you will be able to benefit from the latest enhancements done by the communities on these methodologies. You will also be able to get help from the respective community should you need it.
- You will be able to focus on the project, and not the process: When you're using a known methodology, you will be able to focus on the project itself and how to make it a success, rather than how to manage the project (because the process to manage the project is already provided by the methodology).
As for disadvantages of project management methodologies, I can think of two:
- Sometimes, project managers insist on using the wrong methodology: Project managers need to assess the needs of their project before choosing a methodology. For example, if you're managing a software project it's probably better to use Agile. Some project managers, instead of studying the needs of their projects to know which methodology to use, choose the methodology that worked for them the last time, and this is bad, because the wrong methodology can potentially result in project failure.
- Methodologies can be inflexible: Regardless of the methodology you're using, sometimes you'll find yourself limited by its barriers. Often, you will find that applying 100% Waterfall or 100% Agile to manage your project is not possible, you will feel that you need to twist the methodology a bit to accommodate your project's needs, but when you do that, you are no longer considered to be using the same methodology, so you may face project management risks (not project risks) that result from not completely adhering to the methodology. This is a dilemma that many project managers face.
So to answer your question "How important is a PM Methodology?" - I'd say (based on the advantages above) that it's extremely important, and it's not possible to manage a real project (by real I mean a project that is at least 3 months long and has more than 3 persons working on it) in this day and age without following a methodology.