There exists a cryptographic technique called split keys which could be used on top of Bitcoin to solve some problems in needing to trust people to make Bitcoin transfers. The idea is for the payor and payee to jointly generate a Bitcoin address that will receive the payment. Bitcoin addresses are essentially public keys, and knowledge of the corresponding private keys are what let you spend the coins. In this case, though, a public key is jointly generated between the payor and payee, such that each only ends up with, in effect, half the private key. Neither party will be able to spend coins sent to the address corresponding to this split key.
The payor then makes a payment of the agreed amount to this special address. Once this is done, the payor has lost the Bitcoins. He can't spend them anymore; they belong to this new address which is split between the two of them. The payee can't spend the coins either, at this point.
To complete the transfer, the second step is for the payor to reveal his part of the private key to the payee. Then the payee knows the full private key, which gives him control of the address that received the payment. They are now his Bitcoins to spend as he likes.
The advantage of splitting up the payment into two steps like this is that the first step, where the payor makes a payment to the split key, represents a very strong commitment on his part to see the deal through. After that step, typically the payee must hold up his end of the bargain and perform some action he is being paid for. Once that is completed, the second step of the transfer occurs and the payee receives his payment.
Throughout, no one has any financial incentive to cheat. The first step does not benefit the payee, and the only way he gets paid is to perform. And the second step does not harm the payor; he is out the coins already and gains no benefit from failing to follow through.
It is analogous to tearing a $100 bill in half and giving half to someone, with a promise to deliver the other half if he cooperates. This is a credible commitment and a strong inducement. You have no financial incentive to cheat him if he holds up his end.