Nikki and Teddy, you guys have really good points. I think there is a thin line between not responding appropriately, and building their independence. This is what Tracy says about independent play:
For 6 to 9 mos:
"This is the age when children first see a connection between their own behavior and a subsequent chain of events and when bad patterns are easily reinforced. When parents tell me that their child of six to nine months cries to be picked up after five or ten minutes of activity, I say, "Well, don't pick her up." Otherwise, you're teaching her that when I make this noise, Mum picks me up. It's not that your child is thinking, Oh, I know how to wrap Mum around my little pinky. She's not consciously manipulating you... at least not yet. Instead of rushing to pick her up, sit next to her and reassure her, "Hey, hey, hey, it's okay. I'm right here. You can play on your own." Distract her with a squeaky toy or a jack-in-the-box."
She goes on to say that you should make sure the crying/whining is not from something else, like overstimulation, and if it is, address that immediately.
I guess I feel that by allowing him to whine if I am nearby encouraging him, I am teaching him to play indepenently while still being there for support and praise. Just as I teach him to sleep on his own but still am there for support, I do the same for playtime. Much of the day, I am by his side interacting with him, but at times, (for example, while I fold clothes), it is important that he be able to calmly play on his own, with smiles and praise from mom. And it is my goal to teach him how to do that.
I totally respect everyone's opinion on this though. I think you need to do what seems right for each kiddo.