Problem: In a T-SQL script, an exception occurs while a cursor is open, resulting in the cursor never being closed. But, the exception handling wraps the entire script, not just the cursor, so there is no guarantee that the cursor will be open if/when the CATCH statement is reached.

Solution: query the sys.syscursors view to see if the cursor(s) in question is still open:

BEGIN CATCH
     ...

     IF EXISTS (SELECT 1 FROM sys.syscursors WHERE cursor_name = 'MyCursor')
     BEGIN
	DEALLOCATE MyCursor
     END
     
     ...
END CATCH

Update 7/14/09

I just tried to deploy this to a development environment, rather than my own computer. There it was running as a user with restricted access. I received the following error:The SELECT permission was denied on the object 'syscursors', database 'mssqlsystemresource', schema 'sys'."

This was easily remedied when I finally discovered the CURSOR_STATUS function:

DECLARE @cursorstatus int;
SELECT @cursorstatus = cursor_status('global','MyCursor')
IF @cursorstatus > -2
BEGIN
	DEALLOCATE MyCursor
END