Allow me to give the obvious answer of spirulina. Here's a NASA report from 1988 on the subject of growing food during space missions. I don't know if it's particularly different from any other NASA report on the subject:
The abstract is unhelpful, but the entire introduction is highly relevant to your question, and provides a broad overview of associated science. This was part of the effort for a particular program at that time. I don't imagine they use the same program name anymore, but a number of species have certainly been cultivated in space since that time.
I'll offer some of the most relevant quotes which answer your question.
Conventional food sources consist of higher plants and animals. Unconventional food sources for human consumption are photosynthetic algae and bacteria and non-photosynthetic bacteria, yeasts and fungi. Conventional food sources are highly palatable, but require a long time to produce. The photosynthetic energy efficiency of higher plants is less than 3%. Algae, on the other hand, grow rapidly; their metabolism can be controlled; they produce a high ratio of edible to nonedible biomass; and their gas-exchange characteristics are compatible with human requirements.
tl;dr: Conventional food is far too inefficient to use, but algae tastes disgusting.
The nutritional quality of all cyanobacteria which have been tested (See Appendix) appears to be very high. For example, Spirulina, in addition to being the richest known source of vitamin B12, also contains significant amounts of vitamins B1 and B2. Similarly, one gram of Spirulina contains one-half of the adult daily requirements of vitamin A (B-carotene). The trace elements and iodine found in cyanobacteria are also important when considering the nutritional quality cyanobacteria.
tl;dr: cyanobacteria (a type of algae) does just fine nutritionally
The most difficult problem in using algae as food is the conversion of algal biomass into products that a space crew could actually eat over a long period of time. If algae are to be considered as a primary food source, it will be necessary to determine that they can be converted into a wide enough range of a palatable complete diet. Therefore, Spirulina, an edible alga with less nucleic acids and no cell walls, offers a good prospect for further studies by manipulating growth parameters.
tl;dr: Spirulina is basically the least disgusting cyanobacteria we can find