I know this has been an issue before but all of the resources I have found relating to solutions have not worked. Maybe someone here can throw in some ideas. I have a new module that I am creating for DNN 04.06.02. The module only has a View control defined. Here is the user control:

ViewTest.ascx:
<%@ Control language="vb" Inherits="Agnitek.Modules.BlakemanWebForm.ViewBlakemanWebForm" CodeFile="ViewBlakemanWebForm.ascx.vb" AutoEventWireup="False" Explicit="True" %>

ViewTest.ascx.vb:
Namespace OurCompany.Modules.Test
    Partial Class ViewTest
        Inherits Entities.Modules.PortalModuleBase
        Private Sub Page_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
            If Not IsPostBack Then
                Dim temp As New LinkButton
                temp.CommandArgument = 1
            End If
        End Sub
    End Class
End Namespace

When viewing this module, the Page_Load Sub runs twice. I previously had server controls on the page and when they would cause a postback, the first time Page_Load is called IsPostBack = true but the second time through IsPostBack=False. This wreaks havoc on my code so I need to figure out why/how I am getting two Page_Load fires.

I have also tried overriding OnInit and OnLoad as follows but these are both called twice as well:
Namespace OurCompany.Modules.Test
    Partial Class ViewTest
        Inherits Entities.Modules.PortalModuleBase

        Protected Overrides Sub OnInit(ByVal e As System.EventArgs)
            MyBase.OnInit(e)
        End Sub

        Protected Overrides Sub OnLoad(ByVal e As System.EventArgs)
            MyBase.OnLoad(e)
            If Not IsPostBack Then
                Dim temp As New LinkButton
                temp.CommandArgument = 1
            End If
        End Sub
    End Class
End Namespace

Any ideas on what to do next?

Are you sure that the page isn't being requested twice for other reasons?  A neat tool to use is microsoft Fiddler, which allows you to watch all requests and responses as they are communicated between your web browser and server.

I had this issue once and it took me FOREVER to figure out that the authentication provider was setting a variable and then issuing a redirect; upon the next load the variable was already set and so it did not redirect but returned the page.