Latex Error: 'Sweave.sty' not found?

The likely reason that this error is triggered is due to the texmf folder not being properly mapped to Miktex's root directory. Since Sweave.sty is positioned in a sub directory of texmf, Miktex never finds it.

Sweave.sty comes standard with current R downloads.

To properly map the texmf directory to Miktex's root directory, follow these instructions carefully.

1. Locate the texmf directory inside the share folder in R. For me, the path was C:\Program Files\R\R-3.0.2\share\texmf but this can change from user to user
2. Launch Miktex's Options via the start menu or by locating this exectuable C:\Program Files (x86)\MiKTeX 2.9\miktex\bin\mo_admin.exe. You can also follow these instructions
3. Click on the "Roots" tab and click "Add"
4. Map the folder path to texmf that you located earlier.
5. If you receive an error about the file being in use, make sure to close out of any open session of TeXworks.
6. Click "Ok" and you're set to go.

Like I said above, this is the straight forward answer to get you out of the forums and exploring Miktek and Sweave.

Enjoy!