Several formats incorporate unique or unusual data structures in their design. These are usually to accomplish the specific purpose of the format or to create as much generality as possible.
A common file format that comes to mind under the heading of "unusual" is TIFF. TIFF contains a rudimentary header, but stores much of its data in a series of tags called Image File Directories, which are fixed in neither size nor position. They are instead like an in-memory list data structure in that they are linked by a series of file offset values. Data can be found by seeking to the next offset from the current offset. While this arrangement can lead to confusion (and indeed TIFF has many times been called a "write-only" format), it allows a programmer to construct a header-like structure that can contain any information at all, thus adding to its versatility.
Unusual or unique features of other formats include the storing of image data and palette information in separate files (the Dr. Halo CUT and PAL files, for example) and the storing of monochrome bitmaps as blocks of ASCII format 1's and 0's (as in the PBM format), designed perhaps with interplatform portability in mind.