Representing several points with same coordinates on map using ArcGIS Desktop?

You can use "cartograpic representations" to display your points. Then use the Disperse Markers tool. Your point coordinates will still the same, only the position of the symbol (=representation) will move.

This requires a ArcInfo license (ArcGIS for Desktop Advanced).

A similar Q&A appears under the title of Is there a tool to add “noise” to overlapping X, Y coordinates so they are no longer in the EXACT same place? - and I think the solutions for that will apply equally well to your situation.

Another option not mentioned yet is aggregating the points at the same location and then displaying points as either proportional to the number of individual events they represent or have categorical point sizes.

This is good for displaying general spatial relationships, but if you have a small number of over-lapping points (and exactness of location is not an issue) I agree the "jitter" of points seems more attractive. Also the jitter of points allows labels for individual events (or different point markers), which aggregation does not.