While I personally have a number of issues with Kohn's book, I do agree that "do-this-and-you-get-that" is a poor system, fraught with problems.
The stance that we are taking with my son (who is still only two, but its never too early to start expecting participation) is that chores are things that just need to get done, and that we expect him to do those chores that he is developmentally capable of.
So far, we're still at the stage where he actively wants to participate, so all that is necessary is to say "would you like to help me feed the cats?" or "would you please put your milk cup in the sink?", and he (usually) eagerly helps out. In fact, since the few tasks we've assigned him so far are very routine, it has gotten to the point where he gets very upset if we don't let him do his part (I once was in a hurry and fed the cats without him, and he was in tears).
For tasks that aren't as routine, there is sometimes resistance, and no doubt this will become an issue at some point with the routine tasks as well, once he gets older.
In those cases, we simply tell him that those tasks must be done, because everyone has things they have to do around the house. Rather than "do this because we say so", we emphasize the consequences of not doing the chores. Not in the form of threats, but rather examples: "if you don't pick up your toys, then you won't be able to find the ones you want, we might trip over them or step on them and hurt our foot, and the house won't look very nice", or "well, the kitties are hungry, and they'll be sad if you don't give them food".
We also point out the things that we do around the house: "mommy and daddy both cook dinner, and clean up the dishes, so we can eat each night and have clean dishes to eat on. Mommy does laundry so we have clean clothes to wear. Daddy takes out the trash so the house doesn't smell bad", etc..
If he refuses to complete routine tasks, then he loses routine privileges. If he absolutely refuses to clean up his toys, we put those toys away and tell him he won't be able to play with them for a while since he can't take care of them.
We also point out the benefits of doing the chores whenever incidental opportunities occur. If my son can't find a specific toy we may point out "see, this is why its a good idea to put your toys away, so you know where they are."
I firmly believe that financial rewards should not be a part of basic chores. An allowance is not a reward for doing what you are supposed to. An allowance is a tool to help teach financial responsibility and the value of money. As such, if you do give an allowance, I would not suggest withholding it as a punishment (although requiring a small portion of the allowance going towards reparation for something damaged may be appropriate).
As such, some small rewards may be offered for tasks that are not routine, but which fall within the child's ability. Shoveling the snow off of the driveway may be worth a few bucks. Holding the ladder and handing mommy or daddy tools when we're fixing something may be worth a small reward. One of my favorite blogs discusses this and other methods of teaching finance to children in great detail.