These pages show a way to read most of the files astronomers will need in their day-to-day work. However, no format is so obscure that it could not be used and there are certainly files out there that will not fall into one of the categories above. Here are some hints:
If it is an ASCII file, often some manual editing will do the job. E.g. in a space-separated table there are missing values:
col1 col2 col3
aaaa 1 2
bbbb 3
cccc 4 5
In a text editor put nan in the empty space and asciitable will read the file.
Google. No file format is too obscure to find a reader for it.
When writing files, use standard formats like FITS, ascii, HDF5 and not your personal, undocumented binary format.