Trusted timestamping on the Bitcoin blockchain
Trusted timestamping allows to prove you held a document, some information or a file at some specific point in time, in a way that can't be forged. Read more at Wikipedia.
Its possible to hash the data you wish to timestamp and turn it into a Bitcoin address. By making a small payment (a satoshi, or 0.00000001 BTC) to it, the payment is stored on the blockchain along with the address you paid to.
Since only the hash is stored on the Bitcoin blockchain, no one can tell what data you stored, but given the pre-hashed data you can prove the data was created prior to the block that contains the payment made to that address.
Update: Bitcoin-qt 0.8.2 doesn't relay transactions with small outputs by default. A lot of miners still accepts those transactions, so it'll work fine in the short-term (and once the transactions is accepted into a block, it'll be part the Bitcoin network forever). This method will be replaced in the future, when it becomes difficult to send those transactions.
IANAL, TINLA. That being said, I believe it will. From a technical point of view, its nearly impossible (much more so than with TSAs) to fake a timestamp created like that. You will probably need to bring a technical expert to testify to that.
Yes. The coins are sent to an address that they can never be redeemed from, effectively taking them out of circulation. However, because its only a fraction of a bitcoin, the effect is minimal. To put this in perspective, creating one billion timestamps is equal to 10 BTC being lost due to someone losing his private keys (which is quite common and happens on much larger scale).