What use cases exist where a developer or a development team want/need to have their code signed?
Digital signatures mean different things on different platforms. If you're writing Windows desktop software then the biggest initial benefit of signing your executables is to get rid of that nasty "Unknown Publisher" warning that Windows has been showing users since Windows XP SP2. On other platforms (Some mobile, Java, Flash, Office VBA Macros etc) signed code is required in order to elevate permissions.
You can make a Windows program self-check its own digital signature to make sure it is valid, which means the EXE hasn't changed at all since it was signed. Most use that as another layer of protection against malware and piracy.
Check out this too :
http://blog.ksoftware.net/2011/07/what-is-authenticode/
What types of code can/should be signed? JavaScript? Java? C++? Are there different types of codesigning for each language/platform?
In theory it is possible to digitally sign any document but most of the time when people are talking about code signing they're talking about MS Authenticode (attaching digital signatures to any PE format file (EXE, DLL, COM, etc) or signing executables for OSX/iOS.
There are different types of signing on different platforms but most will use the same certificate.
Is the code signed as raw source or the compiled binary?
In most contexts, a binary.