SSDs are reliable enough if you get a decent one, and decent ones that exceed the PS3s SATA 2 (I think) interface can be found for $100 for a 120GB.
I should perhaps have said reliable
and cheap, or just not bothered with the reliable part, as they're supposedly about there overall now. You can pick up a 250 GB SATA II 2.5" drive for a third of that price, although you could probably happily get one of the older, now-obsolete SSDs cheap-ish, since the PS3 doesn't take advantage of recent developments anyway. However, for a lot of PS3 games (i.e. ones with no install or cache usage), SSDs just don't make that much of a difference, either.
As such, I think SSDs are still a stretch at this point, so we probably won't see them in PS4s as standard, except perhaps for the possibility of a later addition of some kind of high-spec version. That would be a strange situation, because games would still have to be made with the "standard" mechanical drives in mind, so hard drive bottlenecks will be avoided in the main anyway.
All of that said, I'd probably get one if I had a PS4, because you just know that a next-gen GT game will be a cache monster, have a sizeable install, and therefore really benefit in load times by having an SSD. Also, for completeness, I learned that SSDs deliberately, to some extent, fragment the data being stored to prevent "wearing out" the flash memory; but their seek times are tiny, and they can do lots of cool things with simultaneous reads from separate areas (probably not universal) so fragmented / random access is not a problem at all.
Finally, I embedded the above-linked video in case browsers baulk at the mobile protocols (like mine did):
