I would love to know how many baseballs are used during an entire MLB season
According to NBC's "Ask Liz" column, MLB says an average of 65 balls are used per game. There are 30 teams playing each other in 162 games each. So there are (15 x 162 = 2,430) games per season, (you have to divide the total number of teams by two, since each game has two teams in it). That equals: (2,430 x 65) baseballs used per season, which totals 157,950 baseballs used during games per regular season.
Update, Dec. 2011:
On p 192 of the paperback edition of his book, "The Baseball: Stunts, Scandals, and Secrets Beneath the Stitches," Zack Hample estimates the answer to this question. Editing out his addition of spring training and post-season games, his answer to the original question would be:
This is 25% higher than my estimate above, and is based on the number of baseballs each team rubs down with Lena Blackburne Rubbing Mud. Note that it represents the number of balls prepared for use, not used in actual games. I'm guessing that prepping 25% more than needed would be overkill, but assuming his number is right, if we split the difference the number would be about 177,375 baseballs per season.
Finally, he says that MLB uses a TOTAL (including batting practice, etc.) of about 1.26 million baseballs per year. At his estimate of $6.79 per ball, that's $8.56 million per year for baseballs (Rawlings says "Thank you").