ArcMap MXD into exe file?

In addition to @PolyGeo's 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).

http://www.dataeast.com/en/carrymap.asp

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