Some coaches believe that you shouldn't go to failure at all- Pavel Whats-his-name is one of them. I think Coach Poliquin also feels you really shouldn't go to failure either (a bit more on that later).
Guys like Platz always went to failure. Mike Metzner advocated always going BEYOND failure. Once you reach failure on your set, you do forced reps, then forced negatives and partials etc...exactly what Pavel tells people to NOT do.
So what is right? Neither and both.
Occasionally I feel it's OK to go to failure. Every few weeks I think it's OK to do the beyond failure thing. But I do not ever constantly go to failure like Metzner and Trevor Smith believe in. I feel that it will actually teach your body (more so your brain) to fail at that number in that exercise. Stretching it? Maybe, but how many times have you been in the gym and tried to squat or similar, and no matter how hard you try, you just can't get that 13th rep? I tend to believe that if you always fail on 12, you have to try adding a few pounds and backing off on the reps or taking weight off and then adding reps. In other words, find a way to trick your body to adapt by adding a different stimulus.
Charles Poliquin says that you should also stop the set if, for whatever reason, you can't reach about 80-85% of your targeted rep range. If you're aiming for 10 reps on the bench press, if you can only do eight with good form, that's OK. But if you struggle on the seventh rep and need help, you should rack it and change exercises. I think his theory behind this, is that it is training your body to fail and you will not succeed if you keep failing. However, certain lifters (and I've done this too) don't care and if they lift and fail-even on a single- they'll just keep going till they do get the rep/lift.
Each person has their own theory. I've tried to apply as many as I can to see what works. Everything of Poliquins has worked for me. Particularly the 80% of failure and quitting. Once, for about 6 weeks I did Incline DB Presses. I would get 8 with the 100's one week. The next week I would get 5 on the second set (I was doing 5 sets) and I would quit and move to my next exercise- thus decreasing my total sets per bodypart from 8 to 5. The next week I did my training with nothing different except perhaps a bit more enthusiasm. I got 10 reps. Next week I moved up to the 105's and the cycle continued. When I failed below my target rep range, I quit and moved on. And again, my reps with the same weight increased.
I've also used the HIT method Metzner advocates, and while I felt more thoroughly exhausted at the end of the set/workout, the only difference I noticed was my weights going down and maybe a bit more detail. Overall, I didn't feel the means justified the end (I think that's the saying!) for me and my goal.