Unless we're talking about an exceedingly small amount of data here, given the price-per-gigabyte difference between SSDs and rotating magnetic media, SSDs make no sense whatsoever for backup.
Look at it this way: You're going to pay ~$200 for 50-100GB of SSD (depending on the quality of the drive), and ~$70-100 for a 1TB-1.5TB HD.
If you have 50GB of data to back up, you could buy two magnetic hard drives for the price of one SSD, back up on both, and if one dies you have a second working one.
If you have 500GB of data to back up, even a single-layer SSD backup is going to cost you on the order of $1000. For that price you could comfortably buy TEN rotating hard drives, put the same data on all ten, buy a fire-safe with the extra you saved, and unless ALL TEN drives fail simultaneously (because somebody EMP'd your house, in which case you probably won't much care about your backup strategy, because you either just got nuked or western civilization was devastated by a geomagnetic storm), you're fine. And of course you'd really want TWO SSDs, since if you only have a single backup things could go horribly wrong if it suffers an infant failure when you need it, or your computer fries it as soon as you hook it up to do a restore, so double the cost.
Or, buy two 1.5TB HDs ($200), a BDR drive ($200), 500GB worth of BD-R or -RE media ($200), make two copies of your data, burn a copy to BDR, put one hard drive in your house, one in a safe deposit box, mail the BDRs to a family member to hedge against EMP attack, upload a full copy of the data to an online backup service, and you STILL probably only spent $800. On a solution that's going to be exponentially more reliable when it comes to data retrievability than even the most reliable SSD on earth.
Me personally, I have one online backup at home and a second HD backup I keep at my parents' house, in case my place gets looted or burns to the ground, plus all the REALLY irreplaceable stuff (writing, mostly) is also stored on a web server with DreamHost. This cost me about $200 for over 1TB worth of backup, plus around $100/year for the few dozen MB of online stuff that I'd be paying anyway for webhosting. I'd put that up against any SSD at a minute fraction of the cost.
Thing is, when people are talking about SSD reliability, they're talking about how likely the drive is to fail while it's being used. Which is entirely different from reliability of something sitting quietly in a box for backup purposes. When people say SSDs are unreliable, they're most likely talking about the fact that an individual cell of an SSD can only be re-written a finite number of times, after which it becomes useless. In some use patterns, with a lot of data being written and re-written (say, a Photoshop scratch disk), this limit might actually come into play, and cause the disk to fail sooner. On the other hand, an SSD is nearly immune to damage due to getting dropped or banged around, so in a laptop it's probably more reliable, at least physically. Similarly, traditional hard drives have moving parts, which do eventually wear out if they're left on long enough and/or turned on and off enough. SSDs are, presumably, significantly less prone to this sort of wear-related failure, on account of having no moving parts.
Further, most SSDs have at least a little overprovisioning--extra, unused storage space to transparently swap in when a cell becomes unusable due to whatever failure occurred, either being overwritten one too many times or a simple component failure. Rotating hard drives have extra sectors, too, but a lot less of them, since the failure rate is lower. The more overprovisioned space in an SSD, the more reliable--at least on paper--it is. The best drives, like the enterprise-grade SandForce-based ones (for example, the top-of-the-line drives from OWC) have something like 30% extra, unused space to swap in--that's a lot (which you of course pay for).
Based on pure MTTF statistics, most "normal" rotating hard drives are in the 1 million hour range (meaning, statistically and based on accelerated testing, that a drive will last an average of 1 million hours). This of course has little to do with reality--1 million hours is 114 years, and it's pretty obvious the chances of a drive lasting that long are just about zip, let alone an average drive lasting that long. The numbers are really only useful for comparisons. OWC's SSDs currently list MTTFs of 2 million hours, which is comparable to a good pro-grade rotating hard drive. (Interestingly, they originally listed 10 million hours on their top-of-the-line RE edition SSDs, but the site now seems to say 2 million on everything.)
All that is to say that, according to manufacturer specs, a very good SSD is somewhere between 2x and 10x as reliable as a decent HD. On paper. In practice, none of these SSDs have been in the wild long enough to have any idea how reliable they'll actually be over time. Probably good, but who knows.
None of that matters, though--the point is, when it comes to the ability to retrieve data, the more copies of your backups you have, the better your chances, and adding copies in other locations or other kinds of media (optical, for example) is that much better. And given the extravagant price-per-GB costs of an SSD, even if they were exponentially more reliable--which is debatable--they'd be a ridiculous choice for backup unless you're filthy rich. And even then, you'd probably do better to have an extra copy on rotating magnetic media instead of two SSDs, on the chance that the SSDs both suffer from the same design or firmware failure after X number of hours.
