As far as I know, there isn't any File/Folder browser control out of the box in Windows Forms nor WPF.
However there are commercial third-party controls that offer a Windows Explorer-like interface to browse files and folders on disk. Take a look at these products from LogicNP:
Alternatively, you could host the Windows Forms WebBrowser control in WPF and use it to browse the filesystem, since it is integrated with the Windows shell.
In XAML you could do something like this:
<Window x:Class="Samples.FilesystemBrowser"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:wf="clr-namespace:System.Windows.Forms;assembly=System.Windows.Forms"
Title="Filesystem Browser">
<StackPanel>
<WindowsFormsHost>
<wf:WebBrowser Url="C:\" />
</WindowsFormsHost>
</StackPanel>
</Window>
Note, that with .NET 3.5 SP1 Microsoft added a native WPF WebBrowser control, so you can optionally use that instead:
<Window x:Class="Samples.FilesystemBrowser"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Filesystem Browser">
<StackPanel>
<WebBrowser Source="C:\" />
</StackPanel>
</Window>