SaaS: Software as a Service
Cloud application services or “Software as a Service”(SaaS) are probably the most popular form of cloud computing and are easy to use. SaaS uses the Web to deliver applications that are managed by a third-party vendor and whose interface is accessed on the clients’ side. Most SaaS applications can be run directly from a Web browser, without any downloads or installations required. SaaS eliminates the need to install and run applications on individual computers. With SaaS, it’s easy for enterprises to streamline their maintenance and support, because everything can be managed by vendors: applications, runtime, data, middleware, O/S, virtualization, servers, storage, and networking. Gmail is one famous example of a SaaS mail provider.
For further reading you can visit wiki’s SaaS explanation here
PaaS: Platform as a Service
The most complex of the three, cloud platform services or “Platform as a Service” (PaaS) deliver computational resources through a platform. What developers gain with PaaS is a framework they can build upon to develop or customize applications. PaaS makes the development, testing, and deployment of applications quick, simple, and cost-effective, eliminating the need to buy the underlying layers of hardware and software. One comparison between SaaS vs. PaaS has to do with what aspects must be managed by users, rather than providers: With PaaS, vendors still manage runtime, middleware, O/S, virtualization, servers, storage, and networking, but users manage applications and data. PaaS provides the computing infrastructure, the hardware, and the platforms that are installed on top of the hardware. Similar to the way that you might create macros in Excel, PaaS allows you to create applications using software components that are controlled by a third-party vendor. PaaS is highly scalable , and users don’t have to worry about platform upgrades or having their site go down during maintenance. Users who benefit most from PaaS include companies who want to increase the effectiveness and interactivity of a large staff. For the needs of larger companies and independent software vendors, Apprenda is one provider of a private cloud PaaS for .NET and Java business-application development and deployment.
Some examples of PaaS include Google App Engine , Microsoft Azure Services , and the Force.com  platform.
For further reading you can visit wiki’s PaaS explanation here
IaaS: Infrastructure as a Service
Cloud infrastructure services, known as “Infrastructure as a Service” (IaaS), deliver computer infrastructure (such as a platform virtualization environment), storage, and networking. Instead of having to purchase software, servers, or network equipment, users can buy these as a fully outsourced service that is usually billed according to the amount of resources consumed. Basically, in exchange for a rental fee, a third party allows you to install a virtual server on their IT infrastructure. Compared to SaaS and PaaS, IaaS users are responsible for managing more: applications, data, runtime, middleware, and O/S. Vendors still manage virtualization, servers, hard drives, storage, and networking. What users gain with IaaS is infrastructure on top of which they can install any required platforms. Users are responsible for updating these if new versions are released.
For further reading you can visit wiki’s IaaS explanation here