If you want to know what kind of files they are so you can add the right extension, and they are old files from the classic Mac OS, you might use a utility like
Quick Change, which will show the Type & Creator codes used to identify files before OS X. I think it will also do batch conversions, so you could add the appropriate extension to a bunch of files at once.
If you don't know what Type & Creator Codes are, Google "Macintosh type & creator codes" for links to several explanations. Unfortunately, it looks like the only complete list of these codes is $20 shareware. But if most of your mystery files are generic graphic files, their Type codes should be obvious, like TIFF and PICT.
Other heavier duty (shareware) utilities for this work include XRay, FileXaminer, and Super GetInfo.