Around this time every year, I start seeing Aglaonema flowers, though usually, in any given summer, only one of my plants flowers. I'm not a big fan of the flowers, and cut them off. (If you don't, you run the risk of mold: it doesn't appear to hurt the plant, but it's unattractive.) It was more difficult to keep up with the plants at work, because they'd all go at the same time.
Flowering Aglaonemas will keep producing new flowers over and over for a few weeks, then resume growth as usual: they don't die back after flowering, or do anything else special. Care doesn't change during this period either, except for the flower-removal.