Moving from Eclipse to IntelliJ was painful mainly because of the keyboard shortcuts that made me so productive in Eclipse have to be relearnt.

1. Moving between occurence.
In Eclipse, this is achieved by placing caret over a class name or an instance, then Ctrl+. or Ctrl+,
In IntelliJ, place the caret on the class name or instance name and press Ctrl+Shift+F7 to mark. Then move to the next/prev occurence by F3 or Shift+F3. To open pop-up window showing all occurences of a certain instance: Ctrl+Alt+F7. After done navigating, press Esc.

2. Showing type hierarchy.
In Eclipse, Ctrl+T.
In IntelliJ,
Ctrl+Alt+U

3. Go to definition
In Eclipse, F3
In IntelliJ, Ctrl+B

4. List all members of a class
In Eclipse, Ctrl+O
In IntelliJ, Ctrl+F12

Comment/Uncomment current line or selection: Ctrl+/ and Ctrl+Shift+/

Rename refactoring to rename any identifier. Can look in comments, text files and across different languages too: Shift+F6
all purpose shortcut is Ctrl+Shift+A

Go to next/prev open tab: Alt+Left/Right
Go to last viewed open tab: Ctrl+Alt+Left/Right.
Go to implementation Ctrl+Alt+B
Go to super class Ctrl+U

More coming up as I discover them