Android Studio/Intellij Idea: "Table of Contents" for a class

IDEA has a tab called "Structure", which shows all the methods, fields, etc. of the currently-open class.

I've just got a Tip of the Day popup in Android Studio helping with exactly this problem.

You can quickly navigate in the currently edited file with Ctrl/⌘+F12 (Navigate | File Structure).

It shows the list of members of the current class. Select an element you want to navigate to and press the Enter key or the F4 key. To easily locate an item in the list, just start typing its name.

Also, as danny117 points out, you can use Alt/⌘+7 to show / hide the same content in a side panel view (shown above in Chris Jester-Young's answer).