You can convert ESRI ADF format to simple JPEG pictures using the total GIS Converter or similar program. You will get a picture that you can view in almost everything, however any underlaying data that were in the ADF image will be lost.
Convert ArcView ARC/INFO coverage data to JPEG bitmap image format.
We found one software available in the database for this conversion.
Microsoft Windows software - convert adf to jpeg on Windows
A converter that is able to transform various GIS file formats
Convert from adf file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.