This post expands upon the contents of the static page on the legalities of emulation
As stated in the main Emulation Legality page, this is a complex issue (and differs across jurisdictions throughout the world). Anyone wishing to make backups of their own games is urged to conduct their own research before proceeding.
Stances towards the use of emulators and images/roms/iso’s differs from country to country, from hardware manufacturer to manufacturer, and from software developer to developer.
Nintendo, for example, provides detailed information regarding that company’s standpoint with regards to the use of emulators and game images: