Is there a tradition or practice involving fasting in Buddhism or Buddhist countries? Many religions have period or specific practice including fasting. I'm aware of the eating prescriptions of monks, but are there traditions or practices involving fasting for Lay-people?

If not in scripture, are there in culturally Buddhist countries?
In Tibetan Buddhism there is a special practice called Nyungne. Essentially it is a practice on Thousand-Armed Chenrezig who is the embodiment of loving kindness and active compassion (the active aspect is represented by his standing not sitting posture, see the picture below).

The practice is done in retreat settings usually for 2,5 - 3 days. From the day one the practitioners refrain from talking and from the day two they fast and do a number of meditation sessions per day, all focused on Chenrezig. I've been told that it should done with someone who has a direct transmission on this practice and who can give fine details about it. Overall, I know many Western practitioners who took part in such retreats so it is definitely not an old-forgotten, exotic ritual.

In general, Nyungne is a purifying practice on the level of body, speech and mind and helps to nurture compassion and loving kindness towards all the sentient beings.