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
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.