Why do I get 800A0E78 errors?

I think we've all seen this one before: 
 

ADODB.Connection error '800a0e78'   Operation is not allowed when the object is closed.   /<file>.asp, line <line>

 
In older versions of MDAC, the error might be slightly different: 
 

The operation requested by the application is not allowed if the object is closed.

 
This error can be caused when you try to access values from an empty recordset or from a recordset that has already been closed. The most common cause, however, seems to stem from calling a stored procedure that does not use SET NOCOUNT ON. See Article #2275 for more info. 
 
A nearly identical, but far less common message: 
 

ADODB.Recordset error '800a0e79'   Operation is not allowed when the object is open.  /<file>.asp, line <line>

 
This can be caused by trying to set a property that needs to be set before the object is opened. For example, trying to set the MaxRecords property of an ADODB.Recordset object after opening the recordset: 
 

<%      set rs = CreateObject("ADODB.Recordset")      rs.open "SELECT columns FROM tablename",conn      rs.maxRecords = 5  %>

 
To fix, the code should be: 
 

<%      set rs = CreateObject("ADODB.Recordset")      rs.maxRecords = 5      rs.open "SELECT columns FROM tablename",conn  %>

 
You might also get 800a0e78 errors from the provider, without much more useful information. If this happens when attempting to connect to the database, please review Article #2126 and compare your connection string to the recommended formats listed.