Several good posts so far but I will add. I have two boys ages 5 and 3. I bought my oldest a NXT Generation toy boy at age 2 1/2 and he shot a lot with it. It has been handed down and he now shoots a Diamond Atomic. I would highly recommend that set-up and there are usually some good buys on Archery Talk or at some archery shops. We go to a lot of shoots (roughly 15-20) a year and sometimes they both shoot and sometimes it is just my oldest. I never try to push but the kid can shoot!!! I try to hold my excitement but my youngest is a better instinctive shooter and I do think that there is merit in starting with a recurve.
I guess I'm a little different. I got my 7 year old a crossbow at age 7 because she was interested in killing a buck. Fast forward 4 hunting seasons and she's killed 3 bucks including a couple studs. This year we're going to use a compound I bought her a couple years ago. She's pulling back 35 pounds and shooting everyday. Pretty sure we're going to hang up the crossbow this year.