||An MXD is only a viewer for data, storing paths to the actual data, symbology the data are displayed with, etc. There is no way in ArcGIS Desktop to export the MXD to a CAD format. There are number of methods to export the data layers displayed in the MXD to CAD formats, but the MXD itself cannot be exported within the ArcGIS Desktop framework.
Depending on the version of ArcGIS you are using, check out Knowledge Base article 31527. This gives instructions for exporting to DXF instead of DWG, but this tool is available at all license levels for AGIS Desktop.
Another option is Export to CAD in ArcToolbox. Another alternative is the Data Interoperability Extension, which has a 60-day evaluation license available.
Guthrie's Arcv2CAD has also gotten excellent reviews over the years.
I see from other posts on this thread that some other vendors have software that will export an MXD to AutoCAD formats. I am curious if the output files contain vector data, and are editable in AutoCAD, or if the output is a raster format that preserves the appearance of the data, but is not editable.