In the Games
Mr. Fuji looks after abandoned and orphaned Pokémon in Lavender Town. He subscribes to Pokémon Fan Magazine. He is not a native of Lavender Town, and there is some speculation that he used to live on Cinnabar Island, as a photo shows him as a friend of Blaine. He is supposedly shy.
When members of Team Rocket killed a Marowak. in the Pokémon Tower, Mr. Fuji marched up to their hideout and started to rant about how Team Rocket was abusing Pokémon. Team Rocket held him hostage till the protagonist rescues him. In gratitute, Mr. Fuji gives the main character a Poké Flute.
Mr. Fuji wishes for the happiness of all Pokémon. He cares for the Cubone that Team Rocket orphaned.
In Pokémon Emerald there are a series of messages left at Faraway Island where a wild Mew can be found. The messages warn that only someone pure of heart will see Mew. The author's name is smudged, but "-ji" is still readable in the Japanese version. It's possible that Mr. Fuji left the message.
In the TCG
It is theorized that he may have been the inspiration for Dr. Fuji from Mewtwo Strikes Back, due to their similar names and history in studying Mew. However, Dr. Fuji is consideribly younger than Mr. Fuji, leading to another theory that the senior Fuji is the junior Fuji's father. However, besides having the same surname and the aforementioned interest in Mew, there is nothing to back this up.