Common File formats
Several common file formats are in regular use in ROM hacking.
Each game console has sprouted multiple file formats in the transfer from cartridge to ROM, because of variations in the type of copier used to import games, as well as the personal preferences of emulator writers. The pages for each console list the file formats most common for ROM files originating from games of that console.
Compressed File Formats
The ZIP file format is perhaps the most common compressed file format. Most emulators open ZIP files natively, and most modern operating systems (including Windows XP and Mac OS X) have utilities for handling ZIP files built directly into the user interface.
More non-ROM hacking specific information can be found at Wikipedia's ZIP file format article.
Several applications (including the SNES9x Debugger) are compressed in 7zip format, a relatively new format. Although quickly gaining in popularity in Windows circles, Linux and Mac OS users have been slow to adopt 7zip, in part because of the lack of easy-to-use archiving and extracting tools.
More non-ROM hacking specific information can be found at Wikipedia's 7-zip article.