I keep a few dozen assorted plants under fluorescent lighting in my basement, because the light isn't very good at the windows. I have always left the light on day and night, but now that I think about it, that is not very natural for plant growth. Would the health of my plants be improved by controlling the light during the night?
A lot of research has been done on this and most of the results vary by species. Every plant has a photoperiod or the number of hours of light it is used to receiving in a day. Short day length plants can have stunted growth as they depend on day length to trigger flowering and fruit/seed production. Day neutral or 12 hour plants like most tropicals can do better. From this site
Most foliage plants originate along the equator, where plants get about 12 hours of high intensity light year-round. Many of these plants grow better under 24 hour light than under 12 hour light as the longer light periods enable plants to compensate for the low intensity of artificial light, by absorbing light over a long period. Certain annual bedding plants may receive enough light in order to bloom indoors under continuous lighting. Some plants that do particularly well under 24 hour lighting are Swiss cheese plant (Monstera deliciosa), coleus, cissus, schefflera and cacti. Continuous light also speeds up growth of many slow growing, flowering plants like orchids and cacti. In this way, they can be brought to maturity much quicker. Some plants do well either both 12 and 24 hour days, including philodendrons, English ivy, pothos and dieffenbachia. Under continuous lighting, they tend to keep their lower leaves longer. Spider plant (Chlorophytum spp) grows best with 12 hours of light.
My interpretation of the research is that tropicals will do fine under 24 hours a day continuous light but plants like tomatoes might suffer. The no risk method is to have the lights on for 20 out of 24 hours.