Clearly depends on how much it matters if your data is lost and the quantity involved.
Hard drives are inherently unreliable and will fail, the only question is when. For small quantities of data (say <1-2TB), for 'reasonable' protection, all that's needed will be one drive with the data and another with a backup - the backup not plugged in at the same time the main drive is plugged in, as much as possible.
If the data is more important then it will be worth having at the least an additional backup, to cover you for when one drive dies and you are left with just the one copy - a vulnerable time otherwise. In this case depending on circumstances you may also wish to keep the backup at a separate physical location when posible, to reduce risk of theft or fire destroying all copies.
RAID is generally not required unless you need online redundancy - the ability to seamlessly keep accessing your data during a drive failure - unusual in a home environment.
Other backup methods like DVD/Blu-ray are generally too much hassle for reasonable quantites of data and will quickly get expensive compared to HDDs too but may be practical for very small amounts.
When backing up larger quantities of data it gets a bit more complicated due partly to hard drive size limitations and the chance of an unrecoverable read error during backup following drive failure. It can become very hard drive efficient to run a RAID 5 or 6 setup, instead of a simple backup, depending on what size hard drives you're using. With 4 or 5 hard drives backed up, if the data isn't too important a RAID 5 array will drastically reduce the number of 'spare' drives needed, from double the number of drives to just 1 extra (or 2 extra in the case of RAID 6). Beware of this being your only backup though as a power spike can destroy more than one drive (possibly all) simultaneously, hence why backups should not be always plugged in.
Realistically for large quantities of important data try to avoid very large volume sizes (>7-8TB) since as the size increases, so does the chance of a further drive failure when trying to re-backup - multiple smaller volumes are better. And as before, at least three copies with one kept offsite is preferable.
Finally, depending on the sort of data you may wish to put a basic encryption on the drives so when they do fail and you get a warranty replacement, you don't have to worry about the warranty company fixing your HDD and viewing your data (although generally I doubt they'd bother as it's expensive - unless they're trying to identify cause of failure, perhaps).
