|All I/O plugins|
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 suprport 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.