Well it really all depends on your application and the RAID level you use. However, in general using RAID provides data redundancy, fault tolerance, increased capacity, and increased performance. Data redundancy protects the data from hard drive failures. This benefit is good for companies or individuals that have critical or important data to protect, or just anyone that's paranoid about losing their gigabytes of MP3s or pr0n.
Fault tolerance goes hand in hand with redundancy in providing a better over-all storage system.
The only RAID level that does not have any form of redundancy or fault tolerance is RAID 0. RAID also provides increased capacity by combining multiple drives. The efficiency of how the total drive storage is used depends on the RAID level. Usually, levels involving mirroring need twice as much storage to mirror the data. And lastly, the reason most people go to RAID is for the increase in performance.