although u can perform any type of recovery while the database in archive log mode and if u have to configure dataguard environment then the database should be in archivelog mode.
database in archivelog mode chance to take hot backup and no data loss in recovery. you can use RMAN for backup and recovery .disadvantage is poor ferformance and more chance to crash disc.
The main advantage of maintaining a database in Archivelog Mode is that it is possible to take the full backup of database while the database is up and running which in turn facilitates the Point In Time Recovery in case of database failure using the archived redologs and last known full backup
RE: What are the advantages of operating a database in ARCHIVELOG mode over operating it in NO ARCHIVELOG mode ?
The one and only thing is that we can perform recovery where as in no archivelog mode we can only perform restore that is previous backup all transactions from then on is lost.