Filemon, Regmon, Process Explorer, et al are fantastic tools, but none of them monitor API access in a way similar to SnoopDos. Microsoft used to ship APIMon with the Platform SDK, but it was a bit flakey. It wouldn't be terribly difficult to write a SnoopDos-like application for Windows, but who has the time? :-) Most Win32 IDEs have some sort of integrated debugger that will show you this kind of stuff. Microsoft's debugging tools (free!) are also good for this kind of thing, but they're not the most user-friendly tools out there.
Trev