In previous releases of OS X, you were able to remove an icon from the dock by just dragging it off. However, this does not seem to work anymore.
How can I remove a program's icon from the dock?
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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.