Compilr, Coderun, and Ideone all look like great in-browser replacements for a full blown IDE. The builds even take as long as a Visual Studio would. They're great for when you want or need the full IDE experience.
But there are many times when a developer might not want that experience. Maybe you're brainstorming a new implementation for an algorithm and you just want to get an idea of what it might look like. Maybe you're in the middle of a presentation and someone in the audience asked you a slightly off-topic question, and you don't want to spin up a new instance of an IDE just to help them understand.
I've been very excited about Roslyn since I heard Anders Hejlsberg speak about it at Microsoft's Build conference, but I never had a use case for it besides the tutorials and samples included with the CTP. One of the cool things that came with the CTP was the new C# Interactive window (a REPL environment) it added to Visual Studio. With it, I can execute C# against my solution on the fly. This is extremely useful for doing things like testing regexes, comparing the results of different method overloads, or quickly testing a method I just wrote, without requiring me to rebuild the entire project or solution.
The idea behind Compilify is to bring that same interactive environment to the web.