I don't think one should go to the point of being stuck at the bottom for every set, but also one should not short himself by giving up "when you think you won't get the weight up if you [go] for it." Weight training is 80% mental and 20% physical, so the fact that you "think" you are at your very last rep is probably in 99% of cases not true.
All that said I feel that training to complete failure is great for bursting through those periods of stagnation in order to tear down your muscles. But on average one should shoot for the last rep with good form, but not 2-3 more reps with good form. Push yourself.