plotting - Extracting the coordinate of a particular point of interest from a ListPlot

Is there a way to obtain the coordinate of a point of interest in a ListPlot?

As an example, I have a list containing many sets of 2D coordinates and the plot drawn is discontinuous at one point (the first derivative is not continuous and the gradient increases suddenly).

Can I extract the location of that point interactively? Otherwise, I have to search through the list of data myself to determine the change of gradient, which defeats the whole purpose of drawing a plot. Also, using the Get Coordinates function from the right click menu does not give very accurate results.

Answer

ListPlot accepts data wrappers besides Tooltip

(although I could not find any mention of this feature in the docs).

So, @Jens' method can be achieved without post-processing:

 data = Table[{Sin[n], Sin[2 n]}, {n, 50}];
 ListPlot[PopupWindow[Tooltip[#], #] & /@ data]

On mouseover:

Click on a point:

Note: Thought this was a new feature added in Version-9, but as @Alexey Popkov noted it also works in version 8.0.4, so it has been around for some time.

Update: A simpler version of @Mr.Wizard's printTip can also be used as a wrapper directly inside ListPlot:

 ListPlot[Button[Tooltip@#, Print[#]] & /@ N@data]

Update 2: Collecting point coordinates:

 clicks = {};
 Column[{ListPlot[Button[Tooltip@#, AppendTo[clicks, #]] & /@ N@data,
   ImageSize -> 300],
  "\n\t", Row[{"clicks = " , Dynamic[clicks // TableForm]}]}]