<p>Is there a standard Java library that handles common file operations such as moving/copying files/folders?</p>

Not yet, but the
New NIO (JSR 203)
will have support for these common operations.
In the meantime, there are a few things to keep in mind.
File.renameTo
generally works only on the same file system volume. I think of this as the equivalent to a "mv" command. Use it if you can, but for general copy and move support, you'll need to have a fallback.
When a rename doesn't work you will need to actually copy the file (deleting the original with
File.delete
if it's a "move" operation). To do this with the greatest efficiency, use the
FileChannel.transferTo
or
FileChannel.transferFrom
methods. The implementation is platform specific, but in general, when copying from one file to another, implementations avoid transporting data back and forth between kernel and user space, yielding a big boost in efficiency.