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.