1. Cloudburst (negative): The failure of a cloud computing environment due to the inability to handle a spike in demand.
   Reference:"The only way to do cloud computing efficiently is to share the cloud - to establish a broad, multitenant grid (or a number of them) that balances the loads of many different companies. Otherwise, it'll be one cloudburst after another, and a whole lot of underutilized capital assets." Source: Nicholas Carr: Intuit's cloudburst frustrates customers.
2. Cloudburst (positive): The dynamic deployment of a software application that runs on internal organizational compute resources to a public cloud to address a spike in demand.
   Reference: "ISV virtual appliances should underpin a new surge in cloud use followed by self-service mechanisms and enterprise connectors enabling organizations to 'cloudburst' to using cloud services." Source: The 451 Group: RightScale rolls its on-ramp toward other cloud systems (subscription required)
   Related uses: Cloudbursting. Reference "In addition to direct sales to enterprises, going forward it hopes that extending out from private clouds to public ones – what we like to call 'cloudbursting' – will become a prevailing IT weather pattern and provide it with additional opportunities. " Source: The 451 Group: Q-Layer has the wisdom to enable private clouds (subscription required)

Cloudstorming: The act of connecting multiple cloud computing environments.
Reference: "...Zimory will be covering off the key cloudy marketplaces and activities: public cloud, internal cloud, cloudbursting (grow-over from internal to public clouds) and cloudstorming (connecting multiple clouds)." Source: The 451 Group: A Cloud for All Seasons

Vertical Cloud: A cloud computing environment optimized for use in a particular vertical -- i.e., industry -- or application use case.
Reference: "The verticalization of the cloud would provide marketing benefits, as Friedman notes, while also providing a possible means of addressing issues of information security crucial to industries such as health care and financial services." Source: Nicholas Carr: The vertical cloud

Private Cloud: A cloud computing-like environment within the boundaries of an organization and typically for its exclusive usage.
Reference: "It is these companies that have dramatically leveraged their internal and originally Private Cloud Computing infrastructures to significant economic benefit. " Source: Kent Langley: Private Cloud Computing: A Few Thoughts

Internal Cloud: A cloud computing-like environment within the boundaries of an organization and typically available for exclusive use by said organization.

Reference: "With Cloud Computing becoming more and more popular, large corporations are likely to set up their own clouds and integrate them with external clouds, like Amazon EC2." Source: Markus Klems: Internal Cloud

Hybrid Cloud: A computing environment combining both private (internal) and public (external) cloud computing environments. May either be on a continuous basis or in the form of a 'cloudburst'.
Reference: "Microsoft would, no doubt, agree. Their "software plus services" approach similarly advocates a hybrid cloud/desktop environment." Source: Kendall Whitehouse: Kevin Lynch: Clearing the AIR

Cloudware: A general term referring to a variety of software, typically at the infrastructure level, that enables building, deploying, running or managing applications in a cloud computing environment.
Reference: "Go to Google Maps, Yahoo Mail, or MySpace — most of Web 2.0, in other words — and you're using  cloudware." Source: Wired: Geekipedia - Cloudware

External Cloud: A cloud computing environment that is external to the boundaries of the organization. Although it often is, an external cloud is not necessarily a public cloud. Some external clouds make their cloud infrastructure available to specific other organizations and not to the public at-large.
Reference: "If an enterprise were to run an app in an external Cloud and wants to connect that to their systems of record in their own datacenters, they might want to consider the same platform in their data centers." Source: Bert Armijo: Pain in the aaSemantics

Public Cloud: A cloud computing environment that is open for use to the general public, whether individuals, corporations or other types of organizations. Amazon Web Services are an example of a public cloud.
Reference: Gerrit Huizenga: Um, Just who is managing your public cloud?

Cloud Provider: An organization that makes a cloud computing environment available to others, such as an external or public cloud.
Reference: "Some workloads, such as application testing and training, are prime candidates for early deployment to a cloud provider due to their transient nature and high Total Cost of Ownership (TCO)." Source: John Janakiraman: Deploying Your Existing Applications to the Cloud

Cloud Enabler: A general term that refers to organizations (typically vendors) who are not cloud providers per se, but make available technology, such as cloudware, that enables cloud computing.

Cloud-Oriented Architecture (COA): An architecture for IT infrastructure and software applications that is optimized for use in cloud computing environments. The term is not yet in wide use, and as is the case for the term "cloud computing" itself, there is no common or generally accepted definition or specific description of a cloud-oriented architecture.
Reference: James Urquhart: The Principles of Cloud Oriented Architecture

Cloud Service Architecture (CSA): A term coined by Jeff Barr, chief evangelist at Amazon Web Services. The term describes an architecture in which applications and application components act as services on the cloud, which serve other applications within the same cloud environment.
Reference: Jeff Barr: The Emerging Cloud Service Architecture

Virtual Private Cloud (VPC): A term coined by Reuven Cohen, CEO and founder of Enomaly. The term describes a concept that is similar to, and derived from, the familiar concept of a Virtual Private Network (VPN), but applied to cloud computing. It is the notion of turning a public cloud into a virtual private cloud, particularly in terms of security and the ability to create a VPC across components that are both within the cloud and external to it.
Reference: "A VPC is a method for partitioning a public computing utility such as EC2 into quarantined virtual infrastructure. A VPC may encapsulate multiple local and remote resources to appear as a single homogeneous computing environment bridging the ability to securely utilize remote resources as part of an seamless global compute infrastructure." Source: Reuven Cohen: Life in the Cloud: Virtual Private Cloud

Cloud Portability: The ability to move applications (and often their associated data) across cloud computing environments from different cloud providers, as well as across private or internal cloud and public or external clouds.

Cloudsourcing - As defined by Dion Hinchcliffe: "Leveraging services in the network cloud to provide external computing capabilities, often to replace more expensive local IT capabilities.Cloudsourcing can theoretically provide significant economic benefits along with some attendant trade-offs. These trade-offs can include security and performance. The term "cloud" represents a set of external services on a 3rd party network, usually the Internet. The services can represent raw computing, storage, messaging, or more structured capabilities such as vertical and horizontal business applications, even community. These services are delivered over the network, but generally behave as if they are local." Read an overview of cloudsourcing by Dion Hinchcliffe.

Cloud Spanning: Running an application in a way that its components straddle multiple cloud environments (which could be any combination of internal/private and external/public clouds. Unlike Cloud Bursting, which refers strictly to expanding the application to an External Cloud to handle spikes in demand, Cloud Spanning includes scenarios in which an applications component are continuously distributed across multiple clouds.