The most common are:
RAID 0
Disk striping; Not fault tolerant; Improved disk input/output (I/O)
RAID 1
Mirrored volumes; Fault tolerant but you basically only get half the storage capacity since it mirrors 1 disk on another (overhead of 50%)
RAID 10
Combination of RAID 1 and 0; Fault tolerant and improved disk I/O, some newer mobo's do this onboard, very nice, but again, only half the storage
RAID 5
Striped volumes with parity; Fault tolerant, even if 1 disk in the set goes down, the system will simply rebuild the data from that disk in memory by using the parity information; Requires a minimum of 3 drives to implement; Excellent read access, moderate write access since it must also calculate the parity info and hence uses more system memory; As with RAID 1, there is some overhead involved, starts off at 33% (you only get ~67% of the overall storage capacity), but the overhead is reduced as you add more drives to the array (25% with 4 drives, 20% with 5, etc), to a maximum of 32 drives
When implementing RAID, there are many factors to take into consideration, disk I/O performance, cost per MB, system memory utilisation etc.
For a home machine, I would find it hard to sacrifice half the storage capacity, unless I absolutely had to have that fault tolerance or I had the extra $ for the 2nd HDD. However, RAID 5 requires a minimum of 3 HDD's and so isn't exactly the most viable option either.
Work machines on the other hand...if I had my way, I'd have RAID 1, or 10 if possible, on my workstation and RAID 5 on my servers.