The following is an example of using JDK7.

public class CopyFileVisitor extends SimpleFileVisitor<Path> {
    private final Path targetPath;
    private Path sourcePath = null;
    public CopyFileVisitor(Path targetPath) {
        this.targetPath = targetPath;
    }

    @Override
    public FileVisitResult preVisitDirectory(final Path dir,
    final BasicFileAttributes attrs) throws IOException {
        if (sourcePath == null) {
            sourcePath = dir;
        } else {
        Files.createDirectories(targetPath.resolve(sourcePath
                    .relativize(dir)));
        }
        return FileVisitResult.CONTINUE;
    }

    @Override
    public FileVisitResult visitFile(final Path file,
    final BasicFileAttributes attrs) throws IOException {
    Files.copy(file,
        targetPath.resolve(sourcePath.relativize(file)));
    return FileVisitResult.CONTINUE;
    }
}

To use the visitor do the following

Files.walkFileTree(sourcePath, new CopyFileVisitor(targetPath));

If you'd rather just inline everything (not too efficient if you use it often, but good for quickies)

    final Path targetPath = // target
    final Path sourcePath = // source
    Files.walkFileTree(sourcePath, new SimpleFileVisitor<Path>() {
        @Override
        public FileVisitResult preVisitDirectory(final Path dir,
                final BasicFileAttributes attrs) throws IOException {
            Files.createDirectories(targetPath.resolve(sourcePath
                    .relativize(dir)));
            return FileVisitResult.CONTINUE;
        }

        @Override
        public FileVisitResult visitFile(final Path file,
                final BasicFileAttributes attrs) throws IOException {
            Files.copy(file,
                    targetPath.resolve(sourcePath.relativize(file)));
            return FileVisitResult.CONTINUE;
        }
    });

In Java 7, there is a standard method to copy files in java:

Files.copy.

It integrates with O/S native I/O for high performance.

See my A on Standard concise way to copy a file in Java? for a full description of usage.