Are you talking about using the same connection across all ASP pages? If yes, then you can store your Connection object in a Session.

First Page
Code:
<%

Dim rs

Set Session("objConn") = Server.CreateObject("ADODB.Connection")
Session("objConn").Open "DSN=DSNName;UID=UserName;PWD=Password"

Set rs = Session("objConn").Execute("Select * From TableName")

'Do recordset operations here

Set rs = Nothing
%>
Second Page
Code:
<%

Dim cm

Set cm = Server.CreateObject("ADODB.Command")

'Execute stored procedure
With cm
    .ActiveConnection = Session("objConn")
    .CommandType = 4    'adCmdStoredProc
    .CommandText = "StoredProcName"
    .Execute
End With

Set cm = Nothing

%>