There have already been some questions about some undocumented functionality in Mathematica. Such as (please add to these lists!)
- How can one find undocumented options or option values in Mathematica?How can one find undocumented options or option values in Mathematica?
- What do these undocumented Style options in Mathematica do?What do these undocumented Style options in Mathematica do?
- Undocumented command-line optionsUndocumented command-line options
Also, other questions and answers that contained undocumented functions
Internal`InheritedBlockInternal`InheritedBlock(also in Exposing Symbols to $ContextPathExposing Symbols to $ContextPath)Internal`Bag(in Implementing a Quadtree in MathematicaImplementing a Quadtree in Mathematica) (also herehere)RuleCondition(in Replace inside Held expressionReplace inside Held expression)
Along with the "Undocumented (or scarcely documented) Features" segment of the What is in your Mathematica tool bag?What is in your Mathematica tool bag? question.
SzabolcsSzabolcs also maintains a list of Mathematica tricks which contains a list of "undocumented stuff".
So, what undocumented functions do you know and how do you use them? (Added useful information is maybe how you discovered the functions and any version dependence.)