There are two separate (and very much potential) 'issues' with SSDs.
1) They rely on firmware which in the past, with specific drives in specific use-cases, has been responsible for various issues including in some extreme cases 'bricking' a drive.
2) All SSDs, because of the nature of NAND, can only sustain a certain amount of writes before they cannot reliably hold a charge and thus become unreliable.
In the case of #1, the extreme cases were mostly some years ago when the industry was much more in its infancy and plagued certain manufacturers in particular who were probably cutting corners in validation (OCZ, for example). Throughout the history of SSDs the likes of Intel, Samsung and others have established very good reputations for reliability (though notably there has been a recent performance issue, now patched, with the popular Samsung 840 EVO: http://www.anandtech.com/show/8617/samsung-releases-firmware-update-to-fix-the-ssd-840-evo-read-performance-bug). Get a good brand and there is no more chance of a critical SSD failure than you have if you buy a traditional mechanical HDD.
RE #2 This issue, and of posted on this numbers of times before, has been massively, massively overblown. Even the lowest endurance SSDs are rated at 1000 writes per block, have overprovisioning and wear levelling algorithms to ensure that writes are distributed evenly. That means the lowest-endurance SSD (say a 120GB drive with 1000 writes), can sustain around 120TB of writes... writes that is remember, not reads. You would have to write (WRITE!) 110GB of data to the drive every day, 365 days a year to reach the endurance rating in 3 years. There have been various posts of people stress-testing drives and reaching 5 or even 10 times more than the reported endurance rating before issues start to arise.
Check out Anandtech's report on the (low endurance) 840 EVO:
http://www.anandtech.com/show/7173/samsung-ssd-840-evo-review-120gb-250gb-500gb-750gb-1tb-models-tested/3
It's just not an issue!
Are there specific use-cases where a consumer SSD is a bad idea, yes (e.g. write intensive databases). Is even the most active computer user likely to exceed the write endurance of a consumer SSD before the drive itself becomes outdated or warrants an upgrade... no, absolutely not.
SSDs are now extremely reliable, get a good brand and you're every bit as safe as you are with a HDD... of course that means you need backups if you value your data... but it's at least as safe as it is on a mechanical disk.