Both brown dwarfs and red giants could host planets. The Sun will eventually expand into a red giant at the end of its life, which will take its surface radius out to somewhere around the orbit of the Earth -- but the outer planets, Mars, and maybe Earth would still survive. Under very different conditions, of course.

Many extrasolar planets have already been discovered around brown dwarfs, red dwarfs, a couple stars much bigger than the Sun, and even neutron stars. There is a full archive of known and confirmed exoplanets here: https://exoplanetarchive.ipac.caltech.edu/

For mappers looking for a shortcut to parsing that database, there's also http://www.hzgallery.org/index.html

A final fun fact: JRR Tolkien didn't like the spelling 'elfs' or 'dwarfs' in his epic, so he introduced 'elves' and 'dwarves' for his fantasy peoples. So when talking about stars, the spelling would be 'dwarfs.'