I would never want a production OLTP or 24x7 database not in archivelog mode. If there is a hardware resource problem, the database doesn't belong on that machine.

You might want to have a Data Warehouse in noarchivelog mode if a backup is taken directly after the data is loaded.

Development databases can be in noarchivelog as long as regular backups are taken and you can tolerate having your developers out of commission for some time.