On your MapView you can set an OnSingleTapListener, and then in your listener's onSingleTap() method iterate through your layers and call getGraphicIDs() with the x and y from the tap plus whatever tolerance is appropriate (I recommend starting with a tolerance of 15 and adjusting as necessary).That is assuming that your layers are of type GraphicsLayer or ArcGISFeatureLayer. If you are using the new FeatureLayer class (just introduced in 10.2) then getFeatureIDs() is the equivalent method to use.
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