The Agile method tries to provide rapid, continuous delivery of product to the customer. Whereas traditional methodologies such as the Waterfall method or other linear processes require detailed requirements that are defined in the beginning where the end product is like what what defined in the beginning. With Agile there is no clearly defined end product at the onset. In Agile there is still a disciplined prioritization process, but the non-static requiremenets, flexibility, constant change, and regular communication approach this as part of the culture and process.

This is most commonly used in software development but the approach can also be powerful in some other types of projects as well. Some users say that practitioners must have lightweight project management processes in place in order to deliver in the short timeframes that Agile demands.

Instead of building the project all togehter, the development is broken up into sprints with small deliverables.

Waterfall methodology is the one that is the most used across all industries. There are many versions of the waterfall method, but the original one included these high-level phases:

1. Requirements specification
2. Design
3. Construction (AKA or coding)
4. Integration
5. Testing and debugging (AKA Validation)
6. Installation
7. Maintenance

Scrum is a type of Agile methodology that focuses around 30-day "sprints" and  monthly "scrum sessions" where project deliverables are broken down into 30-day intervals. When teams switch to scrum, those previously paralyzed by heavy "process" or difficulty in prioritizing work, can see great gains in productivity.

In scrum, there is no title of project manager. Instead there is a "Scrum Master" whose role is to facilitate the daily project communications and tackle any distractions that are trying to interfer with team members ability to do work on the project.

Scrum is applicable only in certain types of environments - mainly those with colocated, 100% dedicated team members (not working of multiple projects), with unlimited support for the project team (not a heavily constrained time and materials budget).

Mostly used in software development, RAD calls for the interactive use of structured techniques and prototyping to define user's requirements and design the final system. This has a cycle of models then prototypes over and over in the process.

Some criticism of this methodology claim that the short interactions don't allow the complex or deep functionality to be thoroughly developed. However with newer, light applications, such as development for Web 2.0 it may be coming back into favor.

NPI is not really a full project management methodology, because it does not include all of the required project management steps that are needed for project success (lacking such things as development of a WBS), but it still is the process that many organizations follow for their product-related projects.

Not a commonly referenced methodology today, but one worth noting because of its familiarity in the service and business traditional approach to project management.

Here is full 868-page paper on the methology.

PRINCE2 is both a methodology and a de facto standard used extensively by the UK Government and is widely recognised and used in the private sector, both in the UK and internationally. This makes it quite different from the Project Management Institute's publication the Project Management Body of Knowledge (PMBOK), which is not a methodology but rather a broad collection of good practices.