The use of RAID really depends all on the situation and specific goals you have in mind. As Casey stated, there are many different levels of RAID, each with their intended purpose, benefit, and disadvantage.
What you are specifically stating is using RAID for protecting data storage on a file server system and not really the purpose of RAID 0 for performance. For data redundancy there are several possible RAID configurations you can choose, but keep in mind that RAID is not a backup solution, it's primary goal is to allow the system to continue running and holding your data in the case of a hard drive failure. You MUST have a solid backup system in place outside of that RAID as, more than once, I've seen RAID systems go down or fail in a way that leaves data destroyed or corrupted.
The simplest and easiest RAID for redundancy for you to set up is going to be RAID1. This can be as simple as taking two large capacity (I'd recommend high quality and even enterprise grade) hard drives and configure them in a mirror with two separate partitions, one for the operating system and one for data. You can even take this a step further to help improve performance a bit and put your operating system on one set of small capacity drives in RAID 1 and another set of large capacity drives in RAID 1 just for your data. This way you can modify your OS RAID array or your DATA RAID array separately from one another without affecting the other.
If you are wanting to get into really high capacities (greater than 2 TB) then you should start looking into other more complex forms of RAID. There is RAID 5 that requires at least 3 drives but you will be able to work with the full capacity of 2 out of the 3 drives. You can also assign hot-spare hard drives if you have an additional spare drive. In the event of a failure, the spare hard drive automatically begins reconstructing the RAID without the administrator needing to swap out drives, reconfigure, or run anything else. RAID 6 is a further adaptation of RAID 5 and requires at least four drives but can sustain failure of two hard drives where all the other RAID levels so far can only protect data from a single drive failure. However, RAID 6 is rather new and only supported on a few server-grade RAID controllers.
Another option mentioned above is RAID 10 which requires at least 4 hard drives, and you will have half of the total drive capacity as usable space, but you gain the benefit of speed from striped data. This can be nice if you have need of a huge amount of disk throughput, but generally file sharing in a small business environment is not going to tax your disk throughput quite that much to need the additional speed of striping. This form of RAID can be configured on more devices than RAID 6 and can sustain failure of two hard drives, but those two drives cannot be in the same striped set or the data is lost.
Finally this brings me to the actual controller. If you're looking at setting up a file server, what kind of hardware will be running this RAID array? Are you looking at a standard desktop system with just the onboard SATA controller, or are you looking at some form of dedicated RAID controller? This is going to make all the difference as well in what form of RAID you can/should consider for your file server.