I am curious if anyone knows of any methodologies that are significantly different (not a recombination) and I would especially appreciate anyone who brought forward any experience with alternatives.
Wikipedia lists these as methodologies/development processes:


Agile - based on iterative and incremental development, where requirements and solutions evolve through collaboration between self-organizing, cross-functional teams.  
Cleanroom - the focus of the Cleanroom process is on defect prevention, rather than defect removal.  
Iterative -  a cyclic software development process developed in response to the weaknesses of the waterfall model. It starts with an initial planning and ends with deployment with the cyclic interactions in between.

RAD -  uses minimal planning in favor of rapid prototyping. The "planning" of software developed using RAD is interleaved with writing the software itself.  
RUP - The Rational Unified Process (RUP) is an adaptable iterative software development process framework, intended to be tailored by selecting the elements of the process that are appropriate.  
Spiral - combining elements of both design and prototyping-in-stages, in an effort to combine advantages of top-down and bottom-up concepts. This model of development combines the features of the prototyping model and the waterfall model.

Waterfall - sequential through the phases of Conception, Initiation, Analysis, Design, Construction, Testing and Maintenance.

Lean -  a translation of Lean manufacturing and Lean IT principles and practices to the software development domain; everything not adding value to the customer is considered to be waste.  
V-Model -  Instead of moving down in a linear way, the process steps are bent upwards after the coding phase, to form the typical V shape. The V-Model demonstrates the relationships between each phase of the development life cycle and its associated phase of testing.

TDD -  relies on the repetition of a very short development cycle: first the developer writes a failing automated test case that defines a desired improvement or new function, then produces code to pass that test and finally refactors the new code to acceptable standards.

