Here is a list of plants that have been grown in space.

Arabidopsis thaliana

A. thaliana is the model organism for plant biology due to its short lifecycle, small size, and useful genomic data.  A. Thaliana was one of the first plants to ever flower in space, in 1982 aboard Soviet Salyut 7.  This plant has been grown on many space missions due to its immense research value.  It is not a viable source of food for astronauts, but the discoveries made using A. thaliana provide insight that can be applied to all varieties of plants.

Learn more: Arabidopsis thaliana

Mizuna Lettuce

Mizuna lettuce has been grown on the International Space Station. This Japanese lettuce was involved in an experiment with water uptake and fertilizer.  You can read about it here:

Mizuna lettuce grown in space

Genome-wide expression analysis of reactive oxygen species gene network in Mizuna plants grown in long-term spaceflight

Zucchini

Zucchini was officially grown in space in 2012 during Expedition 30/31 on the International Space Station.  The zucchini was grown in a plastic bag and nutrient solution, using aeroponics.  The medium of transfer was still water, but was in the form of a fine mist, and therefore basically air.  This was to reduce a large volume of water from being used. Astronaut Donald Pettit created a blog about growing a space zucchini, which you can read here.

 

this list is currently being expanded