A lot of the information you're getting from other people is highly subjective and possibly misinformed when it comes to current-generation SSDs. SSDs have begun to surpass HDDs in a few key reliability measures (see quotes below). And personally, I've seen more than half of the HDDs I've owned or used at work fail--some were DOA, and others lasted anywhere from a month or two to 10+ years. I suspect that most people (especially laptop owners without SSDs) are using progressively-failing HDDs but just aren't aware of it because bad block reallocation works transparently and most people don't run SMART diagnostics.
Early SSDs were plagued by firmware bugs that caused total data loss and, perhaps to a lesser degree, poor write-leveling algorithms which led to premature failure. That said, HDDs are not immune to such firmware bugs, as was demonstrated in one of Seagate's popular product lines a few years ago (which also resulted in total data loss for the unluckiest of Seagate customers).
The two types of drives are very different when it comes to conditions that are likely to result in failure. For example, HDDs are highly prone to damage from overheating or shock, while SSDs have a limited number of write cycles (in more poetic terms, they die a little inside every time you write them). Fortunately, newer SSDs have improved wear-leveling algorithms which attempt to distribute out the writes across the entire drive.
Wikipedia has some interesting notes on the reliability of SSDs vs. HDDs:
SSDs have no moving parts to fail mechanically. Each block of a flash-based SSD can only be erased (and therefore written) a limited number of times before it fails. The controllers manage this limitation so that drives can last for many years under normal use.[109][110][111][112][113] SSDs based on DRAM do not have a limited number of writes. However the failure of a controller can make a SSD unusable. Reliability varies significantly across different SSD manufacturers and models with return rates reaching 40% for specific drives.[86] As of 2011 leading SSDs have lower return rates than mechanical drives.[84]
and
HDDs have moving parts, and are subject to potential mechanical failures from the resulting wear and tear. The storage medium itself (magnetic platter) does not essentially degrade from read and write operations. According to a study performed by Carnegie Mellon University for both consumer and enterprise-grade HDDs, their average failure rate is 6 years, and life expectancy is 9–11 years.[114] Leading SSDs have overtaken hard disks for reliability,[84] however the risk of a sudden, catastrophic data loss can be lower for mechanical disks.[88]
For what it's worth, MTBF is often advertised but is not necessarily considered a good indicator of expected longevity. One vendor could see 1 out of every 15,000 drives fail in 100 hours, while another vendor has 1 out of every 1500 drives fail after 1000 hours. AFR (Annualized Failure Rate) is touted as being a more realistic reliability measure.
Regardless of which one storage technology you decide on, it will fail eventually if you use it (and perhaps even if you don't use it)--this is the unfortunate reality we live in. Your best bet is to buy a reputable brand known for its reliability, and perform frequent backups or continuous backups of your most important files. A continuous backup solution could range from a cloud file-sharing system like Dropbox/Google Drive/SkyDrive to a dedicated continuous backup solution like CrashPlan/Carbonite/Mozy.