This functionality is not available by default in Mathematica, but it is easy to implement a practical version of it. With a little more work you could implement the same thing W|A has, but since that version is mainly better in presentation only, I won't bother with it.
First, you can use W|A directly form Mathematica. Try
== plot sin(x)
But I think this is not what you're looking for.
Try right clicking any graphics object, and choosing Get Coordinates in Mathematica. It'll show the coordinates of the point you hover. You can click several points to mark them, and copy their coordinates using Ctrl-C.
It is possible to customize this functionality using the CoordinatesToolOptions
option.
f[x_] := Sin[x]
disp[{x_, y_}] := {x, f[x]}
Plot[f[x], {x, 0, 10},
CoordinatesToolOptions -> {"DisplayFunction" -> disp, "CopiedValueFunction" -> disp}]
This version will display the function value in place of the
$y$ coordinate.