Realtime data security - This is the main reason for Level 1 RAID; it provides data protection by duplicating all data from a primary drive on a secondary drive. The second drive is an exact copy of the first drive. Data is written to both drives at the same time. In the event one drive fails, the other drive is an exact duplicate.
No additional partition letters - In Windows Explorer, you do not "see" the second drive's partition letters.
Improved Read Times - During a read, only one drive is typically accessed, but the controller can use both drives to perform two independent accesses. Thus, mirroring improves positioning performance. However, once the data is found, it will be read off one drive; therefore, mirroring will not really improve sequential performance.
Realtime data security - RAID Level 1's greatest asset is also it's greatest liability. In the event that you screw up something like your Operating System (been there, done that), it's likely that the backup is also screwed up.
Additional wear on second drive - If only weekly backups are performed, the second drive would see only occassional use, but RAID 1 would have the second drive used just as often as the main drive.
Slower write times - During a write, both hard disks are used and performance may be slightly worse than it would be for a single drive.
Less storage space - For example, with two 60GB drives, the total usable storage space is 60GB and not 120GB.
I tend to tinker and tweak my Operating System (Windows XP) a lot. A couple of weeks ago I nearly corrupted my system with a bad driver install. Life would have been much easier if I had a backup handy. With RAID Level 1, I would have corrupted the second drive as well as the main drive. For me, a weekly backup is more appropriate. However, if data security is paramount, then RAID Level 1 may be exactly what you need.
Additional Resources -The following are good resources for additional information about RAID and provided background for some of the items above