As you mention in a comment, you're populating this data with a DataSet.
The screenshot shows normal behaviour in SSRS 2005 and SSRS 2008.
I created a report in 2005 and 2008 with 4 parameters; two with type Text and two with type DateTime.
Two are populated with a DataSet based on:
select date1 = cast('01-jan-2013' as datetime)
union all select date1 = cast('01-feb-2013' as datetime)
The other two have a default value of =Today()
.
You can see that behaviour is almost identical between versions.
2005:
2008:
The only difference is that the Text parameter doesn't convert a date implicitly.
From your perspective the main things to note are that when the parameter is populated by a DataSet, you can only choose from a dropdown of the available values (i.e. what you're seeing in your screenshot), but if the parameter is not popluated from a DataSet (dropdown) you can choose from the calendar picker as expected.