Mae West said that too much of a good thing is wonderful. For we shipbuilders who write numerical code that is certainly true of speed and accuracy. How seldom we find ourselves in the happy situation of a piece of code that is both fast enough and accurate enough! A colleague and I were chatting about speed and accuracy today and I realized that when I am building software, I prefer a piece of code that is accurate but slow over one that is less accurate but faster. With profiling and careful thought applied to new code, it’s usually pretty easy to make it faster. Addressing a wide-spread numerical issue often requires a complete re-think.
If I am simply using the software (rather than build it), then all bets are off; it depends on what I am trying to do.
Nathan Brixius 
The next generation processor will make accurate code faster. It won’t make fast code more accurate.
Great point, Paul.