Try this:
<TextBlock Text="{Binding PropertyPath, StringFormat=d}" />
which is culture sensitive and requires .NET 3.5 SP1 or above.
NOTE: This is case sensitive. “d” is the short date format specifier while “D” is the long date format specifier.
There’s a full list of string format on the MSDN page on Standard Date and Time Format Strings and a fuller explanation of all the options on this MSDN blog post
However, there is one gotcha with this – it always outputs the date in US format unless you set the culture to the correct value yourself.
If you do not set this property, the binding engine uses the Language property of the binding target object. In XAML this defaults to “en-US” or inherits the value from the root element (or any element) of the page, if one has been explicitly set.
Source
One way to do this is in the code behind (assuming you’ve set the culture of the thread to the correct value):
this.Language = XmlLanguage.GetLanguage(Thread.CurrentThread.CurrentCulture.Name);
The other way is to set the converter culture in the binding:
<TextBlock Text="{Binding PropertyPath, StringFormat=d, ConverterCulture=en-GB}" />
Though this doesn’t allow you to localise the output.