Got a Remington bolt action s/s .22 targetmaster and a Montgomery Wards .410 pump on the same X-mas morning at age 9. Hunted everything from squirrels, rabbits, doves, crows, first 4 whitetails and an occasional grouse with that .410. I agree with the poster that said a .410 teaches you to point and not swing. Money was very hard to come by in my household so you either learned how to hit what you were shooting at or... starve.
Moved up to a Remington 11-48 (12) at age 12 and continued the quest to put food on the table until I went off to college. Loved that spring recoil in those 11-48's - very little felt recoil even to a 12 y/o.
I do respectfully disagree with the poster that said you shouldn't introduce a kid to shooting until age 12. By then the video games and sports and peers and life's many other distractions have allready taken over the kid's priorities. My kids (all 5) have been in the woods (started in a bowhunting treestand) by age 4. This early start has kept them all interested in shooting and hunting for more than 12 years (and counting). Never take them when conditions are bad, so as not to leave a bad lasting impression of Mother Nature. But short increments and lots of encouragement helps them get past the fidgets and the loud voices that most start with. I logged 100+ days in the field last year with my kids. Some days we shot something, some we did not. But every one created lasting memories that can never be taken away.
My kids started shooting a Garcia Bronco .410 with 2-1/2" #6 shot at age 6-7 depending on their size. My oldest boy (9) carries a Charles Daly youth 20g pump w/ choke tubes. It really is a sweet gun at only 4lb - 10oz. Dad keeps threatening to carry it while walking up and down those hills in Shawnee State Forest grouse hunting.
To each his own... but I'm a 3rd generation Hunter's Saftey Instructor and I feel that kid's should be introduced to shooting and hunter safety as early as their personalities allow. BB guns first (allthough we treat every gun -BB, Rifle, Shotgun, Squirt or Capgun the same) SAFE is SAFE and once you teach them the rules of safe handling, then the curiosity and temptation of abusing the priviledge is gone. My 5 y/o twins are just starting to read but can quote you the top 10 rules of safe firearms handling verbatim. And not just what they are - but the why's and how's behind each rule. I'm more comfortable in the field with them than alot of adults that I've hunted with.