The SqlException has a Number property that you can check. For duplicate error the number is 2601.
catch (SqlException e)
{
switch (e.Number)
{
case 2601:
// Do something.
break;
default:
throw;
}
}
To get a list of all SQL errors from you server, try this:
SELECT * FROM sysmessages
Update
This can now be simplified in C# 6.0
catch (SqlException e) when (e.Number == 2601)
{
// Do something.
}