Suppose that I have a new machine so I want to compare it to the older one. I would like to conduct a mean comparison of a parameter, to verify if these 2 machines produce the same results or not. How many results should I have in order to obtain a good statistical power? (more than 80%).
Depends on the standard deviation of the data. If the data are noisy, you will typically need more data than if they were not. It also depends on the size of the difference you hope to detect. Smaller differences require more data. Here is a plot demonstrating this relationship. You can see holding the difference in means constant but increasing the standard deviation increases the required sample size.
There are dozens of these calculators on the web or in languages like R.