What makes blockchain technology so attractive to non cryptocurrency applications? I have often seen articles claiming bitcoin's demise is iminent but yet others state the blockchain technology that powers it is being considered for other uses. What features make it attractive for those purposes versus alternatives?
There are two basic categories of applications for the type of distributed ledger technology behind Bitcoin.

The first category are public systems like Bitcoin, Ethereum, and Ripple. These are systems with no central authority that provide open access to the world. The blockchain technology ensures eventual agreement on the state of the system so that changes in that state (whether they represent payments or something else) can be agreed upon. Anyone can participate in these networks so long as they follow the rules, with the rules being enforced by the software ignoring people who violate those rules.

The second category are private/permissioned systems. These are systems that don't require a central authority for their day-to-day operation. They are generally run by a group of interested parties which formally manages group membership. The blockchain technology gives them data replication. Byzantine fault tolerance (protection even if some of the participants are malicious), and eventual (typically very rapid) agreement on the state of the network. The cryptography also ensures that the past is tamperproof and provable.