As I posted on a similar question, the rules of optimisation are:
1) Don't optimise
2) (for experts only) Optimise later
When is optimisation premature? Usually.
The exception is perhaps in your design, or in well encapsulated code that is heavily used. In the past I've worked on some time critical code (an RSA implementation) where looking at the assembler that the compiler produced and removing a single unnecessary instruction in an inner loop gave a 30% speedup. But, the speedup from using more sophisticated algorithms was orders of magnitude more than that.
Another question to ask yourself when optimising is "am I doing the equivalent of optimising for a 300 baud modem here?". In other words, will Moore's law make your optimisation irrelevant before too long. Many problems of scaling can be solved just by throwing more hardware at the problem.
Last but not least it's premature to optimise before the program is going too slowly. If it's web application you're talking about, you can run it under load to see where the bottlenecks are - but the likelihood is that you will have the same scaling problems as most other sites, and the same solutions will apply.
edit: Incidentally, regarding the linked article, I would question many of the assumptions made. Firstly it's not true that Moore's law stopped working in the 90s. Secondly, it's not obvious that user's time is more valuable than programmer's time. Most users are (to say the least) not frantically using every CPU cycle available anyhow, they are probably waiting for the network to do something. Plus there is an opportunity cost when programmer's time is diverted from implementing something else, to shaving a few milliseconds off something that the program does while the user is on the phone. Anything longer than that isn't usually optimisation, it's bug fixing.