I was recently asked to list 5 must for a cloud computing job. It can greatly differ for roles and kind of industry that you work for. Innovation and rapid delivery is a must for a software developer or 
architect while managing virtual environments and data management skills are necessary for a data center manager. However, I think there are a few common factors that will be applicable for all
Understanding of IT as a Service
One of the advantages for cloud offering is the service model or the shopping cart kind of experience where IT managers shop for the service using their credit card instead of building it themselves. IT managers have to transition from owner of the service to provider of the service. They have to give out their control and focus more on negotiating service quality with appropriate vendors. Prospective candidates transitioning to a cloud domain must understand cloud categories and deployment models. Understanding the business beyond the technologies and identifying ways and means to fulfill business requirements to maximize the productivity of their end-users is a common trait they should demonstrate. Analyst Peter Christy at the Internet Research Group refers to this as inversion of enterprise IT from an application-centric to a people centric structure.
Managing Virtual Environments
Be it a developer or an IT manager, at some point in your transition time, you will have to deal with virtualized environments. You should be proficient in designing and managing IT infrastructure using hosted services, managing policies and configurations within private or public cloud as needed. These skills will help an IT manager to negotiate their SLAs correctly and realistically.
Innovation and Rapid Delivery
Probably one of the most appealing aspects of the cloud computing is the agility with which one can realize their solutions. This is particularly true for developers as well as IT managers. They can fulfil business requirements via innovation and integration of cloud services with agility. Gone are the days where one raise a purchase request and wait for the approvals and subsequent delivery of hardware and software.
Security
One of the drawbacks of not having complete control over the services that you offer is security. This can be a daunting task if the services are offered from a public cloud. One should know how to manage security and compliance and should be familiar with various compliance requirements across verticals and locations. Good understanding of applications delivered from the cloud, the way users accessing them and security implications of the whole model will be a must have trait for a cloud engineer. Analyst Mark Diodati at Gartner says that the shift to the cloud and the consumerization of IT have complicated the task of identity and access management in the enterprise security environment. Federation protocols, OAuth, REST, SCIM, BYO{D,I,A} etc are a few keywords that they can research on.
Data Management Skills
Most organizations will have a hybrid cloud approach where they will have data managed from on-premise and off-premise. Most medium and large enterprises prefer to keep their critical data such as identity and IP related information on-premise. Candidates opting for a cloud computing job must possess necessary skills to design systems to manage and integrate data from off-premise to on-premise. This would also include ability to get deeper understanding of data through analytics and management through big data technologies.
This is no way a comprehensive list of skills. I believe the above items are the intersection of skills and technologies that every individual must possess before adopting cloud technologies or services.