First, we ran across this factoid: about 630 grapes go into making a typical 750ml bottle. The statistic comes from Terry Armentor of Heck Estates, owner of Valley of the Moon winery, Kenwood Vineyard, Lake Sonoma Winery and Korbel as reported here.
Another calculation from Eno Wines estimates that the number of grapes used to make a bottle is in the 440-660 range.
149 Grapes in Your Glass
If we stick with the 630 number, it means each glass of wine takes 126 grapes to make, assuming you pour five glasses from a bottle. That's about a 5-ounce pour. A more generous 6-ounce pour translates into 149 grapes.
2500 Grapes in a 3L Box
To put the numbers in terms of boxed wine, a standard 3-liter box would take just over 2500 grapes. Considering the compact size of a 3L box, that certainly seems like a lot of grapes. According to the Eno stats, that would be about 50 average "clusters," or more than 11 pounds of grapes.
While certainly these numbers vary by the varietal, the winery, their techniques, and so on, they emphasize the amazing value offered by wines that are affordable but still enjoyable. There's a lot of fruit in that bottle!