RAID 0 - data is split between disks (striping) in xKB chunks. The size is usually setable during creation. Yes this can improve performance if the request is at greater than 1x the chunk size. Writes are also spread across the disks so they can be improved as well. No fault tolerance - 1 drive fails and you're hosed. All data on BOTH disks is unusable. Somewhat more expensive usually as you need 2x the drives but 1/2 the size.
RAID 1 - all data is written to both disks (mirrored). The biggest benefit here is fault tolerance. If a disk goes out, the other's there will all the data. Read requests can be faster (if the controller/driver is done right) - 2 disks get the request the first one to have it available wins. Writes are SLOWER. Because you have to do 2x the number of writes. Also expensive - 2x the cost. Mirroring is really handy if you need to backup a database while running. The right controller/software setup will let you "break" the mirror. This creates a snapshot of how the disks looked at that moment in time that can be backed up. Since databases are updating the same files constantly, backups tend not to like them. After the backup, you re-merge the mirrors replacing the snapshot with the current data. An alternative is a product like Verirtas's Advanced filesystem (also called OnlineJFs for HP-UX). This let's you do things you can't normally do while the filesystem is mounted, like extend/decrease it, or create snapshots where the actual fs isn't written to but the new writes are held on another partition waiting - very useful for backups! Don't know if Veritas is available for Linux though - never tried to find it - it can get rather expensive last one we bought was like $10K but it's saved more than that in downtime.
RAID 5 - Data is written to to X (X >= 3) number of disks (stripe plus parity) in x bits instead of x KB of data. You get ((X - 1) * size) in capacity - ie. you lose 1 disk for the parity. If you lose a drive the controller rebuilds the lost information by using the parity information. Lose 2 drives at the same time - all data is gone. Read and writes are spread across multiple drives, but the information is slightly larger for the parity bits. Cost is higher than RAID 0 but less than RAID 1 for the drives - thew controller is another thing and can cost more than the drives. Look for a controller with a RISC processor on it liek an Intel i960. This off-loads the parity burden to the controller. Also look to see if you can get one with onboard RAM cache - to further increase speed. If you're worried about data lose most good RAID-5 controllers allow a hot-spare. These drive hang around until needed. When a drive fails the controller puts the hot spare into action and rebuilds while continuing to run.
RAID 0+1 (RAID 10) - (striped and mirrored) Required 4 Drives minimum - get 2x the drive size in storage - the most expensive, disk wise. Reads faster, writes helped by striping, hurt by mirroring. Somewhat useful when you need a large amount of space (greater than what 1 disk will give you) and need redundancy as well. This is the configuration recommended by Oracle for OLTP applications.