The OME Bio-Formats plugins provide support for over 130 file formats in microscopy, medical imaging, and related life science formats. Bio-Formats is included with the Fiji distribution of ImageJ. See also the Bio-Formats list of supported formats.
ImageJ has some built-in support for the DICOM format, and there are also plugins for working with DICOM files. See the DICOM page for full details.
The HDF5 update site enables support for reading and writing HDF5 image data. Note that HDF5 is a very broad specification; the HDF5 plugin will not support all manner of HDF files, but only those written according to its constraints.
- The ImageJ Documentation Wiki page FAQ: Which file formats are supported by ImageJ (though it is outdated).