I actually like fail pics, just most of the time they are either unoriginal or slapped onto an already well known image. It's pointless to see the exact same picture posted as
1) the original
2) a fail pic
3) and EPIC fail pic
4) a demotivator
5) a demotivator with EPIC FAIL: Because regular failure wasn't enough
In cases 2-5, no additional humour is added. Countless examples are out there, but again, you can think about that security camera in my previous post.
HOWEVER, modifications of fail can be more original. Failbear is a good example; I don't find a bear falling in the middle of the sky as funny as I do by the personification of "Failbear is ready for action". It's the type of randomness that works, but more importantly, adds SOMETHING (even if you don't find the addition funny, you can atleast appreciate that it is different).
Same with "Shipment of fail". I actually like it. But again, It's NOT just "fail" pointing out the failure; it's trying to bring flavour to the fail (by pointing out the ridiculousness of delivering failure). Many disagree with me, but NOTICE THAT THIS IS NOT JUST "FAIL". THERE IS MORE TO IT.
On occasion, demotivators of fail can be funny too. I personally find this fail poster to be funny (this is probably the most controversial one). The idea of starting a fire out of cornflakes and milk can be understood by itself, but I do like the addition of "Sometimes you have no excuse". It works for me.
Finally, fail pictures can be used appropiately to add great insult and personal attacks. In the other thread, I laughed when bobbtjoe posted this as a response to someone's arguement iirc; was it a real arguement on bobbtjoe's part? Of course not. But was it a completely silly, insulting reaction and a troll? Yes!
Even better are aelf's and mise's satirical fail pictures. Aelf's mockery of the entire fail genre in MS paint are beautiful works of art, and clearly attack anyone posting images with "FAIL" on them.
Fail can work at just being offensive toward taboo subjects. The internet is not afraid to insult everything and everybody. Think something as sad as a cemetery can't be laughed at? Slap FAIL somewhere on there! It can be done right; for instance, I find this amusing:
Notice how none of these simply have textual "Fail" slathered on them. The closest are the Jesus and the Star Wars pictures; The Star Wars image is not funny by itself, but is useful as a humourous troll response to something. The Jesus picture has the word "Fail" incorporated INTO the picture, and that is the basis of the joke. The joke relies on previous knowledge of "Fail" pictures, so that one can laugh at the crucifiction (which few people laugh at in a pure form). So, regardless whether you find these funny or not, they try to ADD SOMETHING to the image, rather than just point out a "fail" (the simpsons one is debatable though, but I think the slogan enhances the image of a burning bowl of cereal).