SSDs are much more expensive. And they do fail. They're not really cost-effective for simple file storage. I just saw a Newegg special for this weekend - 4TB spindle drive for $120. That same money will get you maybe 128GB or possibly 256GB in an SSD.
I use SSDs for my system files (for the speed, and fast boot-up), and conventional HDDs for storage. I have 6 Corsair SSDs, in both 128GB and 64GB flavors for my various desktop machines. They seem to work well.
Online storage companies like IDrive or Carbonite are probably the most cost-effective. I personally use SOS online, and I'm paying $75 a year for 100 GB.