I think the default client should show at least one additional digit by default, and of course there should be the option to increase it arbitrarily.
The 0.3.21 release (I hope to have a release candidate available today) will support full-precision values-- you will be able to send 1.00123456 BTC, if you like.
Sending less than 0.01 BTC still requires a 0.01 BTC fee, though. Changing that to "sending less than 0.01 BTC requires a 0.001 BTC fee" might be worth thinking about, but I think there are higher priorities on the core bitcoin TODO list.