Some applications are more easily adapted or are just plain better running in the Cloud than they are hosted or running locally. Some people don't necessarily subscribe to this notion, however after looking as some of the reasoning behind this, it may make a bit more sense. Realizing that not only are some applications more easily put in the Cloud, others may be more difficult or nearly impossible to put entirely in the cloud (without substantial changes to code). Games, CAD, and other video intense applications are good examples of hard to move applications. Non-web enabled video intense enterprise applications are becoming fewer today than compared to even 5 years ago, however they are still out there and the Cloud can only host the backend for applications of this sort, the rendering side has to be done locally. It is important to note that companies like Citrix have developed technologies that allow applications like this to render intense video remotely, but in the overall public Cloud there just isn't much traction for this (although there is a great deal of traction within the walls of the enterprise). There are many applications that don't require this level of intense video, which is what is being focused on here. Business applications commonly have low rendering requirements, but have all sorts of other complex architectural requirements. Let's look at a few of these requirements and how the Cloud can help solve them.

The Scaling Story
Many successful business application implementations end up growing in the number of users and uses rapidly over time. This usually causes scalability issues and a great number of headaches for architects and administrators. In a Cloud based environment, it is trivial to throw a few additional resources at an application either on a temporary or permanent basis. This isn't so easy in a traditional environment giving the Cloud a distinct advantage in its flexibility and associated costs. By being able to leverage resources outside of the walls of the datacenter for specific needs on demand, a business application's response time SLA can be kept far easier than before.

Data Storage
Many SANs today are on a constant churn of storage space, changing partitions, hot and cold LUNs (for those unfamiliar with LUNs, think of specific chunks of space on the SAN), and a complex infrastructure to manage and secure. This is the reality of storage in data centers today. In a cloud storage scenario, these issues are left up to the cloud provider and the track record of cloud based storage is pretty good and steadily improving. Because of the ability to create storage grids under the covers, storage cloud providers can lower their costs, increase their storage space utilization, and easily add additional storage ahead of space and performance demands.

Databases
Commonly databases require complex and redundant systems with many systems either over utilized or underutilized. Most medium to large organizations use DBAs (DataBase Administrators) to managed and maintain their databases. Properly implementing and managing a database is not an easy task and with constant updates, patches, and performance tuning required, it is expensive. The cloud can provide a great alternative to running a database in house, the only drawback is your data doesn't reside on premise. For some companies, having their data locally is a must or in some cases required by law. Most companies have several databases that could be moved into the cloud without risking catastrophic loss or legal action.

Network / Connectivity
Some companies pay out high dollars for fast and reliable connectivity either from one location to another, whether that be an office to another office or from one datacenter to another. This scenario may or may not include internet connectivity. All of these network connections are pricey to implement and maintain, mostly due to the cost of the networking equipment and the network administration required to manage them. Performance and reliability for internet based applications can be very important to companies that rely on the web as a primary channel for revenue. Moving to a cloud provider can in many cases offer greater response times and availability than attempting to run a server either locally or co-located in a local hosting facility, all while not having to give up administrative control over the server (whether it be physical or virtual).

Centralization
By centralizing applications in the cloud, management applications can potentially become more uniform (this depends on what management application(s) are being used. The ability to spin up additional instances to provide better performance, greater concurrency, or redundancy for brief or long periods of time is a prime benefit to the centralization of the cloud. Other benefits of centralizing include the ability in some cases to replicate tiers in other geographic locations and to be able to control tiers through one centralized security policy.
Conclusion
Applications that are running in the cloud have many distinct advantages especially as resources become scarce - (whether they are compute or personnel). Small to medium sized businesses can benefit from offerings in the cloud for mission critical applications more rapidly than enterprises, primarily due to the great expense that most enterprises have already invested toward building out data centers of their own and potentially privacy and regulatory requirements. There are however pockets within enterprises which have specific projects or needs which can easily (and in a non-disruptive way) leverage the cloud and its benefits without necessarily violating IT standards. For small and medium sized businesses, the classic example of an easily accepted need is that of cloud application provider Salesforce.com which has been highly successful and offers a feature rich solution completely in the cloud, giving sales groups easy collaboration, lead generation management, contacts management, etc. Salesforce has been so successful with their sales application, that they branched into other applications such as support.
Depending on what the needs are and what current applications are out there to meet those needs, the Cloud can be a powerful and cost effective tool to leverage no matter the size of the organization.