What type of layers do you have in the data frame (map)? Do you see coordinates in the bottom right of the area where the map is? Are you in layout view or data view? Do you get any results when you click on the data frame with the info tool
A coordinate system is not required for the Go To XY tool to work.
Being in Layout view as Dan Patterson mentioned, will limit the functionality (no graphic elements seem te get added, but flash works).
In case you don't see this interface appear in ArcMap, I might be because you have worked earlier with two displays and it may be showing on the other (not connected) display. If this is not the case, you might need to remove the Normal.mxt or consider installing ArcGIS again...
Did it ever work?
If it didn't and you have removed your profile, get someone else to log on to your computer... if they have no problems, then it is still your profile... if they can't use the tool, then I suspect it is your computer installation (or the monitor issue)
in any type of Layer it doesn't work. Yes while moving the cursor I can see coordinates in the status bar. both in data and data view it doesn't work. the info tool works fine but only when I click in xy tool it doesnt show any thing.
I think the XY tool is hidden beyond the monitor's frame. Are you using dual monitor? Dual monitor can cause such issue. If not, also try changing the resolution of the screen.