Is it possible to send someone a bitcent without a fee? How old would the coins have to be in order to do so?
To avoid fees, the coins you spend should be at least 1 "bitcoin day" old. A 3 BTC input that is 4 days old is 12 "bitcoin days" old. Like "man hours" - 3 men working for 4 hours each is 12 man hours.
So to send 1/100th of a bitcoin for free, it needs to be 100 days old.
To send 24 bitcoins for free, they need to be 1 hour old.
If any of your outputs are less than 0.01 BTC (including any change output), then you will always need to include a fee.
This is to avoid the recommended fee, of course. If you edit the source you can send any amount you like without a fee, but miners may then decide not to include your transaction in a block.
Edit: if you have a 1 BTC coin that is 1 day old, you will be able to send 0.01 BTC (with 0.99 BTC change) without paying a fee. It's the size and age of the inputs that matters, not the outputs. Though the outputs have to be a bit cent or more to avoid fees.
Edit2: and it's not really the age that matters, but the number of confirmations. If we get 1 block every 10 minutes then the above is true.