We are developing an application using Silverlight and WCF Services. Is using Spring.Net is beneficial for us?
>> "Is using Spring.Net is beneficial for us?"
I think the spirit of your question is really geared more towards questioning the benefit of using an IoC/DI framework versus manually managing dependencies as needed. My response will focus more on the why and why not of IoC/DI and not so much on which specific framework to use.
As Martin Fowler mentioned at a recent conference, DI allows you to separate configuration from usage. For me, thinking about DI in the light of configuration and usage as separate concerns is a great way to start asking the right questions. Is there a need for your application to have multiple configurations for your dependencies? Does your app need the ability to modify behavior by configuration? Keep in mind, this means that dependencies are resolved at runtime and typically require an XML configuration file which is nice because changes can be made without requiring a recompile of the assembly. Personally, I'm not a fan of XML-based configuration of dependencies as they end up being consumed as "magic strings". So there's the danger of introducing runtime errors if you end up misspelling a class name, etc. But if you need the ability to configure on-the-fly, this is probably the best solution today.
On the other hand, there are DI frameworks like Ninject and StructureMap that allow fluent in-code dependency definitions. You lose the ability to change definitions on-the-fly, but you get the added benefit of compile time validations, which I prefer. If all you want from a DI framework is to resolve dependencies then you could eliminate XML-based frameworks from the equation.
From a Silverlight perspective, DI can be used in various ways. The most obvious is to define the relationship of Views to ViewModels. Going deeper, however, you can define validation, and RIA context dependencies, etc. Having all of the dependencies defined in a configuration class keeps the code free from needing to know how to get/create instances and instead focus on usage. Don't forget that the container can manage the lifetime of each object instance based on your config. So if you need to share an instance of a type (e.g. Singleton, ManagedThread, etc.), this is supported by declaring the lifetime scope of each type registered with the container.
I just realized at this point I'm ranting and I apologize. Hope this helps!