Is there any way to make an ArcMap mxd doc into a simple exe file so that one who does not have ArcGIS can view my work?
It's not an *.exe but you can either:
- export your map to a layered PDF so that anyone with the free Adobe Reader can view it
- use the Publisher extension to publish your map as a PMF so that anyone with the free ArcReader can view it
In addition to @PolyGeo second suggestion, there is an extension called CarryMap. It does what you exactly want. It exports your MDX into an exe file that can be opened with a double-click; no other software is needed. Furthermore, it exports your map for use in Android or iOS devices as well! However, you should pay to have the extension (commercial extension).