How can I remove an icon from dock in ML?
This is actually still possible; however, a safe-guard to protect novice users has been added. There is now a minimum distance that you need to move the icon away from the Dock for it to be removed.

Once that distance is reached, the cursor will show a wrinkled paper icon.

Simply release the mouse then, and the icon will be removed from the dock normally.

Alternatively, one can still use the context menu of the icon (right-click or long-left-click the icon to make it appear) and go to Options > Remove from Dock.