There is no one size fits all for project methodologies. In most cases, teams choose to use a hybrid of several methods depending on the size, nature and complexity of the engagement on hand. Here is a quick reference list to the most commonly used and proven project management methodologies:
Agile: Short iterations of work are delivered with little upfront documentation of specs or requirements. Frequent delivery aims to ensure visibility of progress, creating opportunities for real -time feedback and changes in scope throughout the life-cycle.
Kanban: Tasks are placed on physical board to create a workflow that shows team members what needs to be accomplished and in what order. The idea is to encourage small, continuous changes and consensus and consensus-based decision-making without the constant oversight of a leader
Scrum: Project leaders create a prioritized backlog of tasks which teams deliver in sprints, implementing group of tasks top-down. Each sprint has a defined timeframe, after which working iterations are shared with the customer, who then offers feedback. Daily meetings, or scrums are used to keep tabs on progress.
Rapid application development: SW development teams quickly produces prototypes, followed by writing small pieces of code with less planning.
Waterfall: Projects progress sequentially through a series of phases beginning with specs or system requirements, and moving through design, implementation, testing and release. Phases can lasts for weeks or months.
source: the Pulse (pmi.org)