An Oracle database can be either in archive or noarchive mode. A production database should definitelly run in archive log mode. Otherwise, the likelyhood to loose data approaches 100%.
A standby database environment requires archive log mode.

Noarchive log mode

If the database is in noarchive log mode, online redo logs can (and will) be overwritten without making sure they are saved. This implies that a database cannot be recovered even if backups were made.

Archive log mode

If the database is in log archive mode, the database makes sure that online redo logs are not overwritten befor the have been archived.
log_archive_dest_n (or, deprecated on EE log_archive_dest ) specify where the archived redo logs go.

Backup after a structural change in the database

After a structural change to the database (such as adding a datafile), a backup is required.

Switching from noarchive to archivelog mode

The database is currently in noarchivelog mode: 
                                          SQL> select log_mode from v$database;

                                          
LOG_MODE
------------
NOARCHIVELOG
Of course, arch is not started. It would wouldn't make sense, after all. 
                                       SQL> show parameter log_archive_start
                                       

                                       
NAME                                 TYPE        VALUE
------------------------------------ ----------- ------------------------------
log_archive_start                    boolean     FALSE
Now, trying to put the db in archivelog: 
                                    SQL> alter database archivelog;
alter database archivelog
*
ERROR at line 1:

                                    ORA-01126: database must be mounted EXCLUSIVE and not open for this operation
Ok, we shut the database down und mount it only (that is we don't open it) to change the log mode. After having changed it, we open the database: 
                                 adpdb:/users/dba/oracle/dba >sqlplus "/ as sysdba"

                                 

                                 
SQL*Plus: Release 9.2.0.2.0 - Production on Tue Jul 29 19:15:42 2003

                                 
Copyright (c) 1982, 2002, Oracle Corporation.  All rights reserved.

                                 
Connected to an idle instance.

                                 
SQL> startup
                                 mount
                                 
ORACLE instance started.

                                 
Total System Global Area  104694832 bytes
Fixed Size                   730160 bytes
Variable Size              54525952 bytes
Database Buffers           49152000 bytes
Redo Buffers                 286720 bytes
Database mounted.

                                 
SQL> alter database
                                 archivelog;

                                 
Database altered.

                                 
SQL> alter database open;

                                 
Database altered.

                                 
SQL> select log_mode from v$database;

                                 
LOG_MODE
------------
ARCHIVELOG

                                 
SQL> show parameter log_archive_start

                                 
NAME                                 TYPE        VALUE
------------------------------------ ----------- ------------------------------
log_archive_start                    boolean     FALSE
SQL>
Still, the arch process has to be started. This can be done via the init.ora file (and a subsequen restart): 
                              
                                 log_archive_dest     = /backup/adpdb/logarch/adpdb_

                                 log_archive_format   = %S.arc

                                 log_archive_start    = true
The important parameter is log_archive_start.
Additionally, arch can be started manually: 
                              
                                 alter system archive log start;

Differences concerning backups

No archive log Archive log
Must backup entire database. Can backup parts of database (datafiles tablespaces)
DB must be shut down. hot backups possible
Only entire DB can be restored Tablespaces can be restored
In case of a failure, all changes sinces the last backup will be lost All commited transactions will be restorable