It's all depends on your business requirement whether the database is on archive log mode or noarchive log.

In case any mishaps like database crash or accedentally deleted table(s) or datafile(s) or tablespace(s) ...

If your business can effort to loose the data from last full backup to the time of mishap then you can put the database in NOarchivelog mode.

If your business needs to recover every thing upto the time of mishap then you should put the database in archivelog mode.

Thanks,