When you try to send coins, you do so by picking inputs (payments you've received) which are equal to or greater than the amount you want to send.  The extra amount is sent back as change to yourself, and sometimes a piece of your inputs are used to pay a transaction fee.

The need to pay a transaction fee is based on the priority of your transaction.  This is determined by the "coin age" of your inputs.  Generally, "1 coin day" worth of age is high enough to avoid fees, as long as the transaction isn't huge.  A "coin day" would be 1 BTC with 144 confirmations, which is the target number of blocks in an average day.  If your input is 0.5 BTC, it would need 288 confirmations.  If it's 0.1 BTC, 1440 confirmations.

There's a few other caveats to a "no fee" default transaction.  These are:  All the outputs are at least 0.01 BTC and the transaction is under 1 KB in size.  Both of these are fairly easy to meet as long as your wallet isn't full of small inputs.

More detail is included here: https://en.bitcoin.it/wiki/Transaction_fees


Keep in mind that these are the default rules.  There's a few other things that can create delays, such as other similar "qualified free transactions" with a higher priority than yours.  By default bitcoind only allocates a specific amount (17 KB IIRC) to processing no-fee + high priority transactions.