UPDATE: Screen Capture
feature was added in IntelliJ IDEA 13 (and Android Studio):
It's available in the Android
tool window (View -> Tool Windows -> Android).
Answer for older IDEA versions:
IDEA doesn't have this feature. If you are on Windows, you can try something like Android Commander or use DDMS directly.
New IDEA versions have a menu shortcut for Monitor (DDMS replacement in recent Android SDK versions):
After running Android Debug Monitor, use the Screen capture button:
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