LabelVisibility

is an option for Callout and Labeled in plotting functions that determines which labels are shown.

Details

	All	always show the label
	Infinity	highest priority for automatic labeling
	n	relative priority for automatic labeling
	-Infinity	lowest priority for automatic labeling
	Automatic	priority determined by ordering
	None	never show the label

With LabelVisibility set to Infinity, -Infinity, Automatic or n, the label will be shown if there is space to put it that does not collide with higher-priority labels or other graphical content.
LabelVisibility->All shows the label even if it will collide with other content.

Examples

Label all the even-numbered points in a plot, even if some of them collide:

Label even-numbered points while avoiding collisions:

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