Waluigi also has the ability to use the Fire Flower, and Wario can manipulate its effect to drastic proportions. It is assumed Wario can use it also.
This article is from the 2006 series of SMBZ and is no longer canon.
Other than the Mario Bros., Sonic has used one as well. In Episode 8, Sonic used a Fire Flower to transform into Fire Sonic. Fire Sonic's powers seem to be much stronger than Fire Mario's attacks, such as the ability to combine it with Chaos Control and can create a pillar of Fire by running in a circle fast and long enough, similar to the tornado attacks used in the games. The attack is supposedly called the Fire Tornado. Like Mario, Sonic also has enhanced strength and speed with this item.