Please add your own entries, and increment the vote count for features that interest you. IMPORTANT: Please try and consider your suggestions from an IntelliJ design and terminology viewpoint rather than trying to insert ideas that are concepts from other browsers that don't make sense in the IDEA world.
Refactoring
Rename method/variables
Extract Method
Extract Variable
Inline method/variable
Editing
Code Formatting (as currently supported for Java code)
Auto insertion of packages and imports (as currently supported for Java code
Code Completion
Intentions support
Syntax Highlighting (including the ability to color Groovy specific constructs differently)
Templating
Live Templates support
Execution & Testing
Ability to run Groovy based tests in a similar fashion to standard JUnit tests, with matching green/red runner results view.
The ability to specify Groovy Run/Debug configurations for scripts and classes. (Scripts shows in the current editor should not require the developer to setup a run/debug config and should be executable via the standard shift-F10/F9 hotkeys.)
Debugging
Full debugging support, including setting breakpoints, watch variables, view stack, view vars in scope, etc.
Support for transitioning from Java to Groovy and vice versa.
Ability to filter stack traces to show only Groovy classes.
Ability to debug scripts in addition to classes.
Misc
Find All References
Type Hierarchy
Groovy Search
Show javadoc
Ability to specify Groovy specific code style
Cross compiler allowing to reference Groovy classes from Java and Java classes from Groovy