There are several advantages to doing this. First and foremost, you can run multiple versions of Office, or a Web browser, on the same desktop. This comes in handy when you are making a transition from an older to newer version and need both to handle incompatibilities. You don't consume individual client licenses for each streaming application. You save on desktop disk storage space and installation issues. And you regain some control over runaway version-itis, too, because your apps are always patched and current, and upgrades are trivial. The downsides is that this is yet another collection of software tools to learn and manage, and they all can be fairly quirky to deal with.
There are three major streaming providers here: VMware's ThinApp, Symantec's Endpoint Virtualization Suite, and Microsoft's App-V. Microsoft and VMware both work best with their own hypervisors, while Symantec's can run on any platform. (To get an idea of how complex these streaming tools are, take a look at a screencast video that I prepared for Symantec here.)
8. Know your licensing costs. With all these products coming together, the ultimate understanding of your software and operating system licensing needs isn't simple. Microsoft has made things harder by saying that VDI deployments will require Windows Virtual Enterprise Centralized Desktop (VECD) licenses. This could be another motivation to get behind application streaming.
As you can see, the universe of VDI is not an easy one to master. But the benefits can outweigh the challenges, and deliver a quick unified desktop platform to a wide installed base if done correctly.