The client only generates new private keys when you create a new receiving address. If you don't do that, the backup can be as old as you want, I believe.
That's incorrect. The client also automatically creates new addresses when you sent money (to send the "change" back to you).
It also automatically generates an address when receiving payment to the currently selected address (or something like that).
Thank you all for the information. For the general public, the client is indeed not the tool to use. At least not in its current form. They would have to use online accounts at web services sites who offer payment processing and will still charge a %ge on every transaction.
Currently several such services exist which are free, eg instawallet.org and mybitcoin.com.