There are tons of theories out there and I'm not sure which is the best yet.
I've been doing a weekly allowance since DS was about 3.5 years old. I followed the $1 per year of age model. He has a chore chart which is basically little things he can help with daily (help make the bed, dress himself, clear the table, clean up his toys, that kind of thing). However, I don't really tie the chores to his allowance and have not yet threatened to withhold his allowance for anything. It's more to give him a feel of what it is like to have money, what a dollar can buy and having a limit on what he can spend.
I don't control his money or tell him what he can't buy. I do give advice (like, if you don't waste your money on that chintzy little thing this week, you'll have double the amount next week to buy something bigger and better, or if you wait until the end of the month, you can buy something really big). In the beginning he didn't get it at all, but now that he's 5, he's really starting to understand the value of things.
I still have him at $4/week right now, haven't bumped him up to $5/week yet. It may seem like a lot, but it's really hard to save up for anything good at much less than that. Most things he wants are in the $15-$20 range and it's very do-able to save up for those types of things within a month. His sense of time doesn't really stretch much further beyond that. Also, as someone online pointed out, $16/month is a heck of a lot less than what I used to spend buying toys for him. Now he's in control of picking out what toy he REALLY wants and how long he's willing to wait for it. It has virtually eliminated all whining in the store.
I'm thinking when I finally do bump him up to $5/week, it will be with the caveat that he save that extra dollar per week for a year, building up to $52 in reserve so he can get a sense of the value of saving. Then we will discuss whether he wants to spend that or continue saving to build up towards something really big.
Anyway, that's my system and it's worked out pretty good for us. However, I'm curious to check out how other people handle this as well. I know we should add in some charity money to our formula too.