You can do that by binding the data sources for the dropdownlist 2 and 3 to the selected Value of the preceding Dropdownlist.
What kind of data source do you use?
You need a data source for each dropdownlist. In VS 2010 (and I think in 08 as well) you can use the data source wizard to configure the parameters for your select method.
For an objectDataSource the markup could look something like this:
<asp:ObjectDataSource ID="GenreSource" runat="server" SelectMethod="GetGenreByType"
TypeName="GenreDao">
<SelectParameters>
<asp:ControlParameter ControlID="DropDown1"
Name="TypeID" PropertyName="SelectedValue" Type="Object" />
</SelectParameters>
</asp:ObjectDataSource>
Event though this might look like actual markup, this is mere pseudocode which is not tested.
The ControlParameter is the key, you can use this method with other DataSources as well.