Not only does it allow you to play those games but it also offers you more features and possibilities than the original machine.
It supports the following ROM formats: NES, NFS, FDS and UNF. If the ROMs are compressed, don't worry it will deal also with those roms compressed as ZIP, RAR and 7z.
FCEUX includes an unusual feature: Multiplayer games through local network or internet. In order to use this feature you'll need to install FCEU server on one of the computers.
Finally, FCEUX allows you to record your games as AVI files or extract the audio as a WAV file so you can listen, view and share how you have played.