Is it feasible to use the Blockchain technology without the Bitcoin?
Blockchain by definition is a data structure, in that sense we can and already have decoupled it from Bitcoin.  There are many alt-currencies that implement blockchain as a data structure and a data store.  

Ethereum is building a blockchain based application platform.   

Storj is an example of blockchain technology that also is trying to create a blockchain for data storage. 

The SAFE(Secure Access For Everyone) network is attempting to build an entire computing platform built on a blockchain.  

The key is incentivizing some form of participation by providing a service. On the Bitcoin blockchain the service being provided is the ability to send value globally very quickly.  Thus the reward that was created is financial.