What's a good way for organizing PDF documents on Windows?

Try Mendeley Desktop: you can tag documents, you can create collections, you can have it automatically sort your PDFs (as well as some other formats) into directories/subdirectories, you can keep bibliographic information that is ready to be used as citation/reference in MS Office and/or OpenOffice.Org resp. Libre Office. You can even sync documents of your choosing (for example several collections) online, and sync them across all of the computers that you have. (Mendeley is cross platform - I'm currently using it on Windows 7 and Ubuntu.) You can even share your collections with other people.

Oh yeah, did I mention that it's free to use. (Up to 500 MB of documents synced and accessible online.) :D

Mendeley Desktop seems great for personal use but you mentioned that you needed it for scientific research. Then maybe you should ask your organization to invest in software like nVivo.

I cannot say much about this particular program, never used it myself, but my friend is using it at her university coupled with tools like EndNote.

One of the interesting features I saw there was a possibility of taking snippets from pdfs, either text or images, and cataloguing them, having each snipped backlinking to the source document. And there is loads more. I suggest watching some videos on youtube to find out more.