Why would someone rent hashing power? I have seen some people on the bitcointalk forum looking for hashing power to rent (here is one example) and usually they pay more to rent the rig than they would earn by selling the mined coins at market price.
It seems to me that they are losing money with the deal so why would someone want to do this? Are there other uses for the hashing power besides bitcoin generation?
The person hopes that the future ratio of how much money they can earn with a given hash power will be more favourable, so they enter a long-term contract.
The person wants to increase the hashrate of a mining pool they own, whether for test purposes or to attract more people with a high hashrate.
The person holds some other cryptocoins and wishes for their price to increase due to higher difficulty the extra hashing power would bring.
The person wants to mine coins, be they Bitcoins or otherwise instead of buying them at an exchange (one may not exist, or the person does not want to use it for some reason).
The person wants to do other activity that can use hashpower for. The person would need to make special arrangements with the owner of the rig, but it could be possible to use the hashpower for generating vanity addresses for example.
The person wants to launch a 51% attack on a smaller cryptocoin network.
To commit money laundering. Renting hashpower is not regulated under anti-money-laundering laws like the exchanges. On the other hand, the mined coins can't be traced back, so they can be sold at any exchange with ease.