I hope I don't upset people with my comments but backup is a serious business and needs to be done correctly. In my opinion, there is only one affordable, reasonably safe way for a home based photographer to backup images and that is to external portable hard disks using automated software.
CD's and DVD's - If you are anything like me then you will have something in the region of 25 - 30,000 RAW files at 25MB each. If I was to backup 25,000 images at an average 25MB each then I would need around 780 x 800MB CD's or 130 x DVD's The storage of all these disks alone is huge and that is without backing up any Jpegs or Tiffs I may have created whilst working on images and that is only one backup. Added to this is the unreliability of CD and DVD's and given that they don't last more than 4 years without degrading it has to be repeated a lot.
Online Storage - Online storage is good in the fact that it is away from your property so any disaster at home and all you need is a computer to get them back. But what if your membership lapses and you hit on hard times and can't afford to renew, where do your images go? in the bin probably after a few months. What if the company goes into liquidation and where are your images really stored and who is accessing them? To many IF's for my liking.
Data Backup Tapes - Easily the best and safest method of backing up which is why this method is still used today in the corporate world. Data tapes can store huge amounts LTO5 tapes hold 1.6TB each of uncompressed data. The drawback though is that they are expensive and you need a server to drive the library and manage the software.
External Hard Disks - This for me is the best method, I use three 1TB portable external HDD and FBackup software which is free from the internet. I run a daily backup which is a mirror of my image store, this runs at 10pm daily and stays with my computer. This secures me against my main HDD failure or accidental deletion of images etc. I then run a Monthly FULL backup of all my data and stagger it between 2 drives so Jan on drive 1 and Feb on drive 2 and so on. I then remove the Jan backup drive and take it away from my home, to my work desk drawer to be precise. and then once Feb backup has completed I swap them over. This secures me against flood, fire theft etc.
Drawbacks, the drives can become full so bigger or additional drives are needed but this is the same for all methods. A drive could be dropped whilst in transit but you can buy hard cases to protect them or just be careful. These drives can fail but then so can tapes or CD's.
I hope this helps