How to check if an object is a certain type

In VB.NET, you need to use the GetType method to retrieve the type of an instance of an object, and the GetType() operator to retrieve the type of another known type.

Once you have the two types, you can simply compare them using the Is operator.

So your code should actually be written like this:

Sub FillCategories(ByVal Obj As Object)
    Dim cmd As New SqlCommand("sp_Resources_Categories", Conn)
    cmd.CommandType = CommandType.StoredProcedure
    Obj.DataSource = cmd.ExecuteReader
    If Obj.GetType() Is GetType(System.Web.UI.WebControls.DropDownList) Then

    End If
    Obj.DataBind()
End Sub

You can also use the TypeOf operator instead of the GetType method. Note that this tests if your object is compatible with the given type, not that it is the same type. That would look like this:

If TypeOf Obj Is System.Web.UI.WebControls.DropDownList Then

End If

Totally trivial, irrelevant nitpick: Traditionally, the names of parameters are camelCased (which means they always start with a lower-case letter) when writing .NET code (either VB.NET or C#). This makes them easy to distinguish at a glance from classes, types, methods, etc.