Взято отсюда.

Предлагается четыре вариант: с рекурсией, без рекурсии и от MSDN (две штуки). На самом деле достаточно двух первых.

1) Вариант с рекурсией

(Просто и изящно. Возможно переполнение стека, но очень маловероятно).

private static void CopyFilesRecursively(DirectoryInfo source, DirectoryInfo target)
{
    foreach (DirectoryInfo dir in source.GetDirectories())
        CopyFilesRecursively(dir, target.CreateSubdirectory(dir.Name));
    foreach (FileInfo file in source.GetFiles())
        file.CopyTo(Path.Combine(target.FullName, file.Name));
}

2) Вариант без рекурсии

(Используется опция SearchOption.AllDirectories. Сначала создается дерево папок, а потом копируются все файлы разом).

private static void CopyFilesRecursively(String SourcePath, String DestinationPath)
{
    // First create all of the directories
    foreach (string dirPath in Directory.GetDirectories(SourcePath, "*", SearchOption.AllDirectories))
        Directory.CreateDirectory(dirPath.Replace(SourcePath, DestinationPath));

    // Copy all the files
    foreach (string newPath in Directory.GetFiles(SourcePath, "*.*", SearchOption.AllDirectories))
        File.Copy(newPath, newPath.Replace(SourcePath, DestinationPath));
}

3) Варианты от MSDN

(привожу для разнообразия, т.к. первых двух вариантов достаточно).

using System;
using System.IO;

class DirectoryCopyExample
{
    static void Main()
    {
        DirectoryCopy(".", @".temp", true);
    }

    private static void DirectoryCopy(
        string sourceDirName, string destDirName, bool copySubDirs)
    {
      DirectoryInfo dir = new DirectoryInfo(sourceDirName);
      DirectoryInfo[] dirs = dir.GetDirectories();

      // If the source directory does not exist, throw an exception.
        if (!dir.Exists)
        {
            throw new DirectoryNotFoundException(
                "Source directory does not exist or could not be found: "
                + sourceDirName);
        }

        // If the destination directory does not exist, create it.
        if (!Directory.Exists(destDirName))
        {
            Directory.CreateDirectory(destDirName);
        }

        // Get the file contents of the directory to copy.
        FileInfo[] files = dir.GetFiles();

        foreach (FileInfo file in files)
        {
            // Create the path to the new copy of the file.
            string temppath = Path.Combine(destDirName, file.Name);

            // Copy the file.
            file.CopyTo(temppath, false);
        }

        // If copySubDirs is true, copy the subdirectories.
        if (copySubDirs)
        {

            foreach (DirectoryInfo subdir in dirs)
            {
                // Create the subdirectory.
                string temppath = Path.Combine(destDirName, subdir.Name);

                // Copy the subdirectories.
                DirectoryCopy(subdir.FullName, temppath, copySubDirs);
            }
        }
    }
}

и еще

using System;
using System.IO;

class CopyDir
{
    public static void CopyAll(DirectoryInfo source, DirectoryInfo target)
    {
        if (source.FullName.ToLower() == target.FullName.ToLower())
        {
            return;
        }

        // Check if the target directory exists, if not, create it.
        if (Directory.Exists(target.FullName) == false)
        {
            Directory.CreateDirectory(target.FullName);
        }

        // Copy each file into it's new directory.
        foreach (FileInfo fi in source.GetFiles())
        {
            Console.WriteLine(@"Copying {0}{1}", target.FullName, fi.Name);
            fi.CopyTo(Path.Combine(target.ToString(), fi.Name), true);
        }

        // Copy each subdirectory using recursion.
        foreach (DirectoryInfo diSourceSubDir in source.GetDirectories())
        {
            DirectoryInfo nextTargetSubDir =
                target.CreateSubdirectory(diSourceSubDir.Name);
            CopyAll(diSourceSubDir, nextTargetSubDir);
        }
    }

    public static void Main()
    {
        string sourceDirectory = @"c:sourceDirectory";
        string targetDirectory = @"c:targetDirectory";

        DirectoryInfo diSource = new DirectoryInfo(sourceDirectory);
        DirectoryInfo diTarget = new DirectoryInfo(targetDirectory);

        CopyAll(diSource, diTarget);
    }

    // Output will vary based on the contents of the source directory.
}