How many times do you blink your eyes in a day?

Every 10-15 seconds. The average person blinks roughly once every 10 seconds. This is a reflex that we can control to a degree (we can stare and decrease the blink rate for a minute or so, or blink rapidly on demand). The tears that lubricate our eyes normally evaporate after 10-15 seconds; blinking "pushes" new tears onto the eye's surface before all the previous tears have evaporated.
At least 20-30x/min. Most people blink, on average, from 20-30 times per minute, at least. Of course this varies greatly depending on the activity. If you're doing activities where you have your eyes open longer at a time (reading, computer work, tv watching, driving), this rate is going to be less).
About 19,200 times. Most people blink their eyes about every three seconds, or 20 times a minute, 1200 times an hour, or roughly 19.200 times in a 16 hour day.