RAID5 is typically used for redundancy. So, if one drive fails, your data is still there. There are some speed benefits as well. RAID5 is also more common for servers than desktops. Minimum drive requirement is 3, but most folks recommend at least 4 plus a failover/hotswap drive.
RAID 1 is not a reliable backup option. If one drive fails or the data gets corrupted, it sometimes gets carried over to the second drive. I've seen this first-hand more than a few times. This requires at least 2 drives.
RAID 1+0 offers spanning and mirroring, though doesn't offer enough redundancy to always survive a failed HDD. 2 drive minimum, 4 recommended.
RAID 0 offers performance, but doubles your changes of data loss since if either drive in the array dies, you loose everything.
There's also JBOD, which effectively spans a partition over multiple drives. But, like with RAID 0, if one drive goes, you lose everything.
So, in addition to the different types of RAID, there's als hardware RAID vs software RAID. Hardware RAID is typically more reliable, less error-prone, has higher throughput, and requires additional hardware to use. Software RAID puts extra load on the CPU, is dependent upon the operating system, and doesn't require a separate piece of hardware.
A hardware-based RAID array can typically be transplanted into another computer without trouble. In most cases, a software-based RAID array cannot.
So, bottom line, hardware RAID5 is usually best for performance and redundancy on an active computer using RAID. Anything less, and you're better off making a separate backup.