There are non-Bitcoin blockchains being created at the moment that are used to trade and transfer assets. It is my understanding that on such a block chain there are "tokens" representing assets such as a share in a company or some other security.
Assuming A wants to exchange with B some assets, how would they create a transaction so that the exchange happens atomically?
A non-atomic solution would be to have A transfer the assets he is selling to B first. Then, B transfers the assets he is paying with back.
Multisig transactions do not seem to solve this problem: One of the signers has to sign first (A). He cannot force B to then sign as well. B might abort the transaction or delay it. This is a trust issue and not atomic.
For a concrete example, A might want to trade a certain Namecoin domain name against another name that is owned by B. This is supposed to be trustless and atomic.